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Journal articles on the topic 'Long walks'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Hartmann, Mark, and Cristina Arguelles. "Transience Bounds for Long Walks." Mathematics of Operations Research 24, no. 2 (1999): 414–39. http://dx.doi.org/10.1287/moor.24.2.414.

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2

Wrigley, John D., Mark E. Twigg, and Gert Ehrlich. "Lattice walks by long jumps." Journal of Chemical Physics 93, no. 4 (1990): 2885–902. http://dx.doi.org/10.1063/1.459694.

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3

Volchenkov, Dimitri. "Infinite Ergodic Walks in Finite Connected Undirected Graphs." Entropy 23, no. 2 (2021): 205. http://dx.doi.org/10.3390/e23020205.

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The micro-canonical, canonical, and grand canonical ensembles of walks defined in finite connected undirected graphs are considered in the thermodynamic limit of infinite walk length. As infinitely long paths are extremely sensitive to structural irregularities and defects, their properties are used to describe the degree of structural imbalance, anisotropy, and navigability in finite graphs. For the first time, we introduce entropic force and pressure describing the effect of graph defects on mobility patterns associated with the very long walks in finite graphs; navigation in graphs and navi

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Patel, Dhruv, Raymond Lin, Barun Majumder, and Vitaly V. Ganusov. "Brain-localized CD4 and CD8 T cells perform correlated random walks and not Levy walks." F1000Research 12 (October 3, 2023): 87. http://dx.doi.org/10.12688/f1000research.129923.2.

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Background. For survival of the organism, T cells must efficiently control pathogens invading different peripheral tissues. Whether or not such control is achieved by utilizing different movement strategies in different tissues remains poorly understood. Liver-localized CD8 T cells perform correlated random walks --- a type of a Brownian walk -- in liver sinusoids but in some condition these T cells may also perform Levy flights -- rapid and large displacements by floating with the blood flow. CD8 T cells in lymph nodes or skin also undergo Brownian walks. A recent study suggested that brain-l

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5

Hammer, Yosi, and Yacov Kantor. "Winding angles of long lattice walks." Journal of Chemical Physics 145, no. 1 (2016): 014906. http://dx.doi.org/10.1063/1.4955161.

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6

Giri, Pulak Ranjan, and Vladimir Korepin. "Quantum search on Hanoi network." International Journal of Quantum Information 17, no. 07 (2019): 1950060. http://dx.doi.org/10.1142/s0219749919500606.

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Hanoi network (HN) has a one-dimensional periodic lattice as its main structure with additional long-range edges, which allow having efficient quantum walk algorithm that can find a target state on the network faster than the exhaustive classical search. In this paper, we use regular quantum walks and lackadaisical quantum walks, respectively, to search for a target state. From the curve fitting of the numerical results for HN of degrees three and four, we find that their running time for the regular quantum walks are followed by amplitude amplification scales as [Formula: see text] and [Formu

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Guinard, Brieuc, and Amos Korman. "Intermittent inverse-square Lévy walks are optimal for finding targets of all sizes." Science Advances 7, no. 15 (2021): eabe8211. http://dx.doi.org/10.1126/sciadv.abe8211.

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Lévy walks are random walk processes whose step lengths follow a long-tailed power-law distribution. Because of their abundance as movement patterns of biological organisms, substantial theoretical efforts have been devoted to identifying the foraging circumstances that would make such patterns advantageous. However, despite extensive research, there is currently no mathematical proof indicating that Lévy walks are, in any manner, preferable strategies in higher dimensions than one. Here, we prove that in finite two-dimensional terrains, the inverse-square Lévy walk strategy is extremely effic

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8

Saiyed, Abrar Ali, Anita Basalingappa, and Piyush Kumar Sinha. "Value Network in Heritage Walks: Case Studies of Ahmedabad City Walks." Journal of Heritage Management 1, no. 2 (2016): 191–204. http://dx.doi.org/10.1177/2455929616687897.

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Long heritage management related activities have been studied by sociologist, heritage management experts, anthropologists and architects and artists. Researchers felt importance of using management theories in heritage management research domain. This paper tries to focus on this call for research. It aims to study the value network in heritage walk organisations for creating shared value - a form of value that Porter and Kramer describe, in placing social and community needs before profit. It studies value network in three heritage walks organized by three organisations in Ahmedabad city in

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9

J., Abhijith, and Apoorva Patel. "Improving quantum spatial search in two dimensions." Quantum Information and Computation 19, no. 7&8 (2019): 555–74. http://dx.doi.org/10.26421/qic19.7-8-2.

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The question of whether quantum spatial search in two dimensions can be made optimal has long been an open problem. We report progress towards its resolution by showing that the oracle complexity for target location can be made optimal, by increasing the number of calls to the walk operator that incorporates the graph structure by a logarithmic factor. Our algorithm does not require amplitude amplification. An important ingredient of our algorithm is the implementation of multi-step quantum walks by graph powering, using a coin space of walk-length dependent dimension, which may be of independ

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10

Chen, Bo, and Ping Ji. "An Exploration of the Triplet Periodicity in Nucleotide Sequences with a Mature Self-Adaptive Spectral Rotation Approach." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/176943.

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Previously, for predicting coding regions in nucleotide sequences, a self-adaptive spectral rotation (SASR) method has been developed, based on a universal statistical feature of the coding regions, named triplet periodicity (TP). It outputs a random walk, that is, TP walk, in the complex plane for the query sequence. Each step in the walk is corresponding to a position in the sequence and generated from a long-term statistic of the TP in the sequence. The coding regions (TP intensive) are then visually discriminated from the noncoding ones (without TP), in the TP walk. In this paper, the beha

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11

Machida, Takuya. "A limit theorem for a splitting distribution of a quantum walk." International Journal of Quantum Information 16, no. 03 (2018): 1850023. http://dx.doi.org/10.1142/s0219749918500235.

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Discrete-time quantum walks are considered a counterpart of random walks and their study has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to two parts. The quantum walker with two coin states spreads at points, represented by integers, and we analyze the chance of finding the walker at each position after it carries out a unitary evolution a lot of times. The result is reported as a long-time limit distribution from which one can see an approximation to the finding probability.

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12

Volchenkov, Dimitri, and C. Steve Suh. "Statistical Mechanics of Long Walks in Dynamic Complex Networks: Statistical Arguments for Diversifying Selection." Dynamics 2, no. 3 (2022): 252–69. http://dx.doi.org/10.3390/dynamics2030013.

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We study the thermodynamic limit of very long walks on finite, connected, non-random graphs subject to possible random modifications and transportation capacity noise. As walks might represent the chains of interactions between system units, statistical mechanics of very long walks may be used to quantify the structural properties important for the dynamics of processes defined in networks. Networks open to random structural modifications are characterized by a Fermi–Dirac distribution of node’s fugacity in the framework of grand canonical ensemble of walks. The same distribution appears as th

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13

Bookout, B. D., and P. E. Parris. "Long-range random walks on energetically disordered lattices." Physical Review Letters 71, no. 1 (1993): 16–19. http://dx.doi.org/10.1103/physrevlett.71.16.

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14

Meunier, Nicolas, Clément Mouhot, and Raphaël Roux. "Long time behavior in locally activated random walks." Communications in Mathematical Sciences 17, no. 4 (2019): 1071–94. http://dx.doi.org/10.4310/cms.2019.v17.n4.a11.

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15

Taylor, Brandon. "Absurd lines, protest walks: notes on Richard Long." Sculpture Journal 18, no. 2 (2009): 176–88. http://dx.doi.org/10.3828/sj.2009.5.

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16

Schnörer, Horst, and Alexander Blumen. "Long-time tails in continuous-time random walks." Physical Review A 41, no. 10 (1990): 5702–4. http://dx.doi.org/10.1103/physreva.41.5702.

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17

Rowan Walrath. "NIH walks back some long COVID grant cancellations." C&EN Global Enterprise 103, no. 9 (2025): 13. https://doi.org/10.1021/cen-10309-polcon2.

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18

Patel, Dhruv, Raymond Lin, Barun Majumder, and Vitaly V. Ganusov. "Brain-localized CD4 and CD8 T cells perform correlated random walks and not Levy walks." F1000Research 12 (January 23, 2023): 87. http://dx.doi.org/10.12688/f1000research.129923.1.

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Background. For survival of the organism, T cells must efficiently control pathogens invading different peripheral tissues but whether such control (and lack of thereof) is achieved by utilizing different movement strategies remains poorly understood. Liver-localized CD8 T cells perform correlated random walks (CRWs)— a type of a Brownian walk – in liver sinusoids but in some conditions, these T cells may also perform Levy flights – rapid and large displacements by floating with the blood flow. CD8 T cells in lymph nodes or skin also undergo Brownian walks. A recent study suggested that brain-

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19

Rokhmatul Hikhmat, Syarifah Lubbna, R. Nur Abdurakhman, and Abas Hidayat. "The effect of morning walk therapy on blood pressure elderly." World Journal of Advanced Research and Reviews 14, no. 1 (2022): 580–83. http://dx.doi.org/10.30574/wjarr.2022.14.1.0371.

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Hypertension is known as the silent killer. Non-pharmacological treatment of hypertension, a morning walk is a light activity suitable for people with the elderly (elderly) to help control blood pressure in the long term. This study aimed to determine the effect of morning walks on changes in blood pressure in the elderly with hypertension in Pabuaran Kidul village, Cirebon, Indonesia. The research design uses a quasi-experiment with a one-group pre-test post-test approach. The sample is 20 respondents. The research instruments used were observation sheets and sphygmomanometer watches. Analysi

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20

Rokhmatul, Hikhmat, Lubbna Syarifah, Nur Abdurakhman R., and Hidayat Abas. "The effect of morning walk therapy on blood pressure elderly." World Journal of Advanced Research and Reviews 14, no. 1 (2022): 580–83. https://doi.org/10.5281/zenodo.7040132.

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Hypertension is known as the silent killer. Non-pharmacological treatment of hypertension, a morning walk is a light activity suitable for people with the elderly (elderly) to help control blood pressure in the long term. This study aimed to determine the effect of morning walks on changes in blood pressure in the elderly with hypertension in Pabuaran Kidul village, Cirebon, Indonesia. The research design uses a quasi-experiment with a one-group pre-test post-test approach. The sample is 20 respondents. The research instruments used were observation sheets and sphygmomanometer watches. Analysi

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21

Reynolds, Andy M. "Bridging the gulf between correlated random walks and Lévy walks: autocorrelation as a source of Lévy walk movement patterns." Journal of The Royal Society Interface 7, no. 53 (2010): 1753–58. http://dx.doi.org/10.1098/rsif.2010.0292.

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For many years, the dominant conceptual framework for describing non-oriented animal movement patterns has been the correlated random walk (CRW) model in which an individual's trajectory through space is represented by a sequence of distinct, independent randomly oriented ‘moves’. It has long been recognized that the transformation of an animal's continuous movement path into a broken line is necessarily arbitrary and that probability distributions of move lengths and turning angles are model artefacts. Continuous-time analogues of CRWs that overcome this inherent shortcoming have appeared in

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22

van Steijn, Leonie, Inge M. N. Wortel, Clément Sire, Loïc Dupré, Guy Theraulaz, and Roeland M. H. Merks. "Computational modelling of cell motility modes emerging from cell-matrix adhesion dynamics." PLOS Computational Biology 18, no. 2 (2022): e1009156. http://dx.doi.org/10.1371/journal.pcbi.1009156.

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Lymphocytes have been described to perform different motility patterns such as Brownian random walks, persistent random walks, and Lévy walks. Depending on the conditions, such as confinement or the distribution of target cells, either Brownian or Lévy walks lead to more efficient interaction with the targets. The diversity of these motility patterns may be explained by an adaptive response to the surrounding extracellular matrix (ECM). Indeed, depending on the ECM composition, lymphocytes either display a floating motility without attaching to the ECM, or sliding and stepping motility with re

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23

Gallotti, Riccardo, Rémi Louf, Jean-Marc Luck, and Marc Barthelemy. "Tracking random walks." Journal of The Royal Society Interface 15, no. 139 (2018): 20170776. http://dx.doi.org/10.1098/rsif.2017.0776.

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In empirical studies, trajectories of animals or individuals are sampled in space and time. Yet, it is unclear how sampling procedures bias the recorded data. Here, we consider the important case of movements that consist of alternating rests and moves of random durations and study how the estimate of their statistical properties is affected by the way we measure them. We first discuss the ideal case of a constant sampling interval and short-tailed distributions of rest and move durations, and provide an exact analytical calculation of the fraction of correctly sampled trajectories. Further in

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24

Videla, Leonardo A. "Out-of-equilibrium random walks." Advances in Applied Probability 52, no. 3 (2020): 772–97. http://dx.doi.org/10.1017/apr.2020.23.

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AbstractWe study the long-term behaviour of a random walker embedded in a growing sequence of graphs. We define a (generally non-Markovian) real-valued stochastic process, called the knowledge process, that represents the ratio between the number of vertices already visited by the walker and the current size of the graph. We mainly focus on the case where the underlying graph sequence is the growing sequence of complete graphs.

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25

Bendikov, Alexander, and Barbara Bobikau. "Long time behavior of random walks on abelian groups." Colloquium Mathematicum 118, no. 2 (2010): 445–64. http://dx.doi.org/10.4064/cm118-2-6.

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26

Konno, Norio, Etsuo Segawa, and Martin Štefaňák. "Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs." Symmetry 13, no. 7 (2021): 1169. http://dx.doi.org/10.3390/sym13071169.

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We connect the Grover walk with sinks to the Grover walk with tails. The survival probability of the Grover walk with sinks in the long time limit is characterized by the centered generalized eigenspace of the Grover walk with tails. The centered eigenspace of the Grover walk is the attractor eigenspace of the Grover walk with sinks. It is described by the persistent eigenspace of the underlying random walk whose support has no overlap to the boundaries of the graph and combinatorial flow in graph theory.

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27

Deng, Kai Ying, and Jing Wei Deng. "Properties and Moving Time Average for Lévy Walks with Power-Law Waiting-Time Distributions." Applied Mechanics and Materials 580-583 (July 2014): 3079–82. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.3079.

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Lévy walks are a natural model for the description of sub-ballistic, superdiffusive motion. The waiting times and jump lengths of Lévy walks are coupled in the form . The-coupling introduces a time cost for each jump in the form of the generalized velocity , such that long jumps get penalized by a higher time cost. In this paper, we firstly investigate the properties of Lévy walks with power-law waiting-time distributions; then discuss its moving time average.

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28

Chisaki, Kota, Norio Konno, Etsuo Segawa, and Yutaka Shikano. "Crossovers induced by discrete-time quantum walks." Quantum Information and Computation 11, no. 9&10 (2011): 741–60. http://dx.doi.org/10.26421/qic11.9-10-2.

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We consider crossovers with respect to the weak convergence theorems from a discrete-time quantum walk (DTQW). We show that a continuous-time quantum walk (CTQW) and discrete- and continuous-time random walks can be expressed as DTQWs in some limits. At first we generalize our previous study [Phys. Rev. A \textbf{81}, 062129 (2010)] on the DTQW with position measurements. We show that the position measurements per each step with probability $p \sim 1/n^\beta$ can be evaluated, where $n$ is the final time and $0<\beta<1$. We also give a corresponding continuous-time case. As a consequence

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29

Cai, Shuiying, Qingyu Huang, Yiwen Ye, Yongxian Wen, and Yunguo Lin. "The sojourn times of one dimensional discrete-time quantum walks." Laser Physics Letters 20, no. 9 (2023): 095210. http://dx.doi.org/10.1088/1612-202x/ace888.

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Abstract In the existing literature, a sojourn time of a discrete-time quantum walk is not a random variable. To solve this problem, we redefine the sojourn time of a quantum walk where its coin evolution operator can be general. We first discuss a class of quantum walks governed by flip operators. We cumulatively calculate how much time a walker spends in the set of non-negative integers up to a fixed evolution time. Whether a walker makes a left or right evolution, we add up the staying times as long as it stays within the target set. We define a sojourn time as the total amount of the stayi

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30

Engelsted, Niels. "General Psychology Walks Again." Journal für Psychologie 26, no. 1 (2018): 74–96. http://dx.doi.org/10.30820/8247.05.

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Explaining the role, importance, and basic layout of general psychology, the paper has two parts. In the first part, told as a ghost story, we visit the long history of general psychology and its usual absence, aka the crisis of psychology. Drawing on the insights of among others George Henry Lewes, Herbert Spencer, Karl Bühler, and Lev Vygotsky, a number of requirements are listed that the author believes are necessary for a general psychology. In the second part is sketched the author’s proposal for such a general psychology. Built on Aristotle’s taxonomy of bio-psyches, the proposal divides

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31

Paradisi, Paolo, R. Cesari, A. Donateo, D. Contini, and P. Allegrini. "DIFFUSION SCALING IN EVENT-DRIVEN RANDOM WALKS: AN APPLICATION TO TURBULENCE." REPORTS ON MATHEMATICAL PHYSICS 70, no. 2 (2012): 205–20. https://doi.org/10.1016/S0034-4877(12)60040-8.

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Scaling laws for the diffusion generated by three different random walk models are reviewed. The random walks, defined on a one-dimensional lattice, are driven by renewal intermittent events with non-Poisson statistics and inverse power-law tail in the distribution of the inter-event or waiting times, so that the event sequences are characterized by self-similarity. Intermittency is a ubiquitous phenomenon in many complex systems and the power exponent of the waiting time distribution, denoted as complexity index, is a crucial parameter characterizing the system’s complexity. It is shown

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32

Yan, Zhiguang, Yu-Ran Zhang, Ming Gong, et al. "Strongly correlated quantum walks with a 12-qubit superconducting processor." Science 364, no. 6442 (2019): 753–56. http://dx.doi.org/10.1126/science.aaw1611.

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Quantum walks are the quantum analogs of classical random walks, which allow for the simulation of large-scale quantum many-body systems and the realization of universal quantum computation without time-dependent control. We experimentally demonstrate quantum walks of one and two strongly correlated microwave photons in a one-dimensional array of 12 superconducting qubits with short-range interactions. First, in one-photon quantum walks, we observed the propagation of the density and correlation of the quasiparticle excitation of the superconducting qubit and quantum entanglement between qubit

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33

Young, Robert. "One Big Union, One Long Fight." Monthly Review 69, no. 6 (2017): 58. http://dx.doi.org/10.14452/mr-069-06-2017-10_7.

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As the global economy grows increasingly unstable, undermining job security and the dignity of work, the IWW's pioneering tactics, and perhaps even the union itself, may again be the means by which working people of all walks secure "the good things in life" while building "a new society within the shell of the old."Click here to purchase a PDF version of this article at the Monthly Review website.

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34

Pfluegl, Wolfgang, and Robert J. Silbey. "Long-time properties of random walks with a single trap." Physical Review E 58, no. 4 (1998): 4128–33. http://dx.doi.org/10.1103/physreve.58.4128.

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35

Bertin, Karine, Soledad Torres, and Ciprian A. Tudor. "Maximum-likelihood estimators and random walks in long memory models." Statistics 45, no. 4 (2010): 361–74. http://dx.doi.org/10.1080/02331881003768750.

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36

Kabatiansky, G., and G. Oshanin. "Finding passwords by random walks: how long does it take?" Journal of Physics A: Mathematical and Theoretical 42, no. 43 (2009): 434016. http://dx.doi.org/10.1088/1751-8113/42/43/434016.

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37

Klafter, J., and G. Zumofen. "Probability Distributions for Continuous-Time Random Walks with Long Tails." Journal of Physical Chemistry 98, no. 30 (1994): 7366–70. http://dx.doi.org/10.1021/j100081a022.

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38

Köhler, G. H., E. W. Knapp, and A. Blumen. "Continuous-time random walks on a long-range hierarchical model." Physical Review B 38, no. 10 (1988): 6774–78. http://dx.doi.org/10.1103/physrevb.38.6774.

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39

Marks, Paul. "Robots could one day enjoy long walks on the beach." New Scientist 212, no. 2844 (2011): 16. http://dx.doi.org/10.1016/s0262-4079(11)63136-9.

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40

Luo, Hao, and Peng Xue. "Properties of long quantum walks in one and two dimensions." Quantum Information Processing 14, no. 12 (2015): 4361–94. http://dx.doi.org/10.1007/s11128-015-1127-5.

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41

Trojan, Bartosz. "Long time behavior of random walks on the integer lattice." Monatshefte für Mathematik 191, no. 2 (2019): 349–76. http://dx.doi.org/10.1007/s00605-019-01316-3.

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42

Mounaix, Philippe, and Grégory Schehr. "First gap statistics of long random walks with bounded jumps." Journal of Physics A: Mathematical and Theoretical 50, no. 18 (2017): 185001. http://dx.doi.org/10.1088/1751-8121/aa65f2.

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43

Zhang, Y. C., and Y. Shapir. "Kinetic growth of polyelectrolytes: Long-range true self-avoiding walks." Physical Review B 33, no. 7 (1986): 4941–43. http://dx.doi.org/10.1103/physrevb.33.4941.

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44

Ecker, Nicolas, and Karsten Kruse. "Excitable actin dynamics and amoeboid cell migration." PLOS ONE 16, no. 2 (2021): e0246311. http://dx.doi.org/10.1371/journal.pone.0246311.

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Amoeboid cell migration is characterized by frequent changes of the direction of motion and resembles a persistent random walk on long time scales. Although it is well known that cell migration is typically driven by the actin cytoskeleton, the cause of this migratory behavior remains poorly understood. We analyze the spontaneous dynamics of actin assembly due to nucleation promoting factors, where actin filaments lead to an inactivation of these factors. We show that this system exhibits excitable dynamics and can spontaneously generate waves, which we analyze in detail. By using a phase-fiel

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45

JEUB, LUCAS G. S., MICHAEL W. MAHONEY, PETER J. MUCHA, and MASON A. PORTER. "A local perspective on community structure in multilayer networks." Network Science 5, no. 2 (2017): 144–63. http://dx.doi.org/10.1017/nws.2016.22.

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AbstractThe analysis of multilayer networks is among the most active areas of network science, and there are several methods to detect dense “communities” of nodes in multilayer networks. One way to define a community is as a set of nodes that trap a diffusion-like dynamical process (usually a random walk) for a long time. In this view, communities are sets of nodes that create bottlenecks to the spreading of a dynamical process on a network. We analyze the local behavior of different random walks on multiplex networks (which are multilayer networks in which different layers correspond to diff

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46

Sakiyama, Tomoko, and Yukio-Pegio Gunji. "Optimal random search using limited spatial memory." Royal Society Open Science 5, no. 3 (2018): 171057. http://dx.doi.org/10.1098/rsos.171057.

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Lévy walks are known to be efficient movements because Lévy walkers search wide areas while restricting returns to previously visited sites. A self-avoiding walk (SAW) is a series of moves on a lattice that visit the same place only once. As such, SAWs can also be effective search algorithms. However, it is not realistic that foragers memorize many visited positions for a long time. In this work, we investigated whether foragers performed optimal searches when having limited memory. The agent in our model followed SAWs to some extent by memorizing and avoiding visited places. However, the agen

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47

Weber, Kyle S., F. Elizabeth Godkin, Benjamin F. Cornish, William E. McIlroy, and Karen Van Ooteghem. "Wrist Accelerometer Estimates of Physical Activity Intensity During Walking in Older Adults and People Living With Complex Health Conditions: Retrospective Observational Data Analysis Study." JMIR Formative Research 7 (March 15, 2023): e41685. http://dx.doi.org/10.2196/41685.

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Background Accurate measurement of daily physical activity (PA) is important as PA is linked to health outcomes in older adults and people living with complex health conditions. Wrist-worn accelerometers are widely used to estimate PA intensity, including walking, which composes much of daily PA. However, there is concern that wrist-derived PA data in these cohorts is unreliable due to slow gait speed, mobility aid use, disease-related symptoms that impact arm movement, and transient activities of daily living. Despite the potential for error in wrist-derived PA intensity estimates, their use

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48

Mykhailova, O. V. "Background. The diverse experience of artistic culture, refl ected in the established system of genres, appears in a new light from the standpoint of modernity as experts." Aspects of Historical Musicology 15, no. 15 (2019): 119–37. http://dx.doi.org/10.34064/khnum2-15.06.

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from different fi elds of art refer to the same topic. Stable repetition of phenomena, the names of which were originally perceived in the poetic and metaphorical way, indicates the formation of a certain genre branch, little developed in scientifi c research. Genre neoformations of this kind include walks, behind the semantic layer of which a certain set of stylistic means shines through. It is not by chance that attempts are made to comprehend this phenomenon in aesthetic and artistic aspects. Objectives. The purpose of the article is to highlight the phenomena of artistic culture with the m

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ALON, NOGA, CHEN AVIN, MICHAL KOUCKÝ, GADY KOZMA, ZVI LOTKER, and MARK R. TUTTLE. "Many Random Walks Are Faster Than One." Combinatorics, Probability and Computing 20, no. 4 (2011): 481–502. http://dx.doi.org/10.1017/s0963548311000125.

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Abstract:

We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the cover time – the expected time required to visit every node in a graph at least once – and we show that for a large collection of interesting graphs, running many random walks in parallel yields a speed-up in the cover time that is linear in the number of parallel walks. We demonstrate that an exponential speed-up is sometimes possible, but that some natural gr

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Posé, N., K. J. Schrenk, N. A. M. Araújo, and H. J. Herrmann. "Schramm–Loewner evolution of the accessible perimeter of isoheight lines of correlated landscapes." International Journal of Modern Physics C 29, no. 01 (2018): 1850008. http://dx.doi.org/10.1142/s0129183118500080.

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Abstract:

Real landscapes exhibit long-range height–height correlations, which are quantified by the Hurst exponent [Formula: see text]. We give evidence that for negative [Formula: see text], in spite of the long-range nature of correlations, the statistics of the accessible perimeter of isoheight lines is compatible with Schramm–Loewner evolution curves and therefore can be mapped to random walks, their fractal dimension determining the diffusion constant. Analytic results are recovered for [Formula: see text] and [Formula: see text] and a conjecture is proposed for the values in between. By contrast,

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