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Journal articles on the topic 'Random walks'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

Blondel, Oriane, Marcelo R. Hilário, Renato S. dos Santos, Vladas Sidoravicius, and Augusto Teixeira. "Random walk on random walks: Low densities." Annals of Applied Probability 30, no. 4 (2020): 1614–41. http://dx.doi.org/10.1214/19-aap1537.

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2

Montero, Miquel. "Random Walks with Invariant Loop Probabilities: Stereographic Random Walks." Entropy 23, no. 6 (2021): 729. http://dx.doi.org/10.3390/e23060729.

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Random walks with invariant loop probabilities comprise a wide family of Markov processes with site-dependent, one-step transition probabilities. The whole family, which includes the simple random walk, emerges from geometric considerations related to the stereographic projection of an underlying geometry into a line. After a general introduction, we focus our attention on the elliptic case: random walks on a circle with built-in reflexing boundaries.

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3

Lee, P. M., and B. D. Hughes. "Random Walks and Random Environments: Vol. I, Random Walks." Journal of the Royal Statistical Society. Series A (Statistics in Society) 159, no. 3 (1996): 624. http://dx.doi.org/10.2307/2983343.

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4

Hughes, B. D. "Random Walks and Random Environments, Volume 1: Random Walks." Biometrics 54, no. 3 (1998): 1204. http://dx.doi.org/10.2307/2533883.

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5

Weiss, George H. "Random walks and random environments, volume 1: Random walks." Journal of Statistical Physics 82, no. 5-6 (1996): 1675–77. http://dx.doi.org/10.1007/bf02183400.

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6

Georgiou, Nicholas, Mikhail V. Menshikov, Aleksandar Mijatović, and Andrew R. Wade. "Anomalous recurrence properties of many-dimensional zero-drift random walks." Advances in Applied Probability 48, A (2016): 99–118. http://dx.doi.org/10.1017/apr.2016.44.

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AbstractFamously, a d-dimensional, spatially homogeneous random walk whose increments are nondegenerate, have finite second moments, and have zero mean is recurrent if d∈{1,2}, but transient if d≥3. Once spatial homogeneity is relaxed, this is no longer true. We study a family of zero-drift spatially nonhomogeneous random walks (Markov processes) whose increment covariance matrix is asymptotically constant along rays from the origin, and which, in any ambient dimension d≥2, can be adjusted so that the walk is either transient or recurrent. Natural examples are provided by random walks whose in

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7

Boissard, Emmanuel, Serge Cohen, Thibault Espinasse, and James Norris. "Diffusivity of a random walk on random walks." Random Structures & Algorithms 47, no. 2 (2014): 267–83. http://dx.doi.org/10.1002/rsa.20541.

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8

Zhang, Yujian, and Hechen Zhang. "Application of Random Walks in Data Processing." Highlights in Science, Engineering and Technology 31 (February 10, 2023): 263–67. http://dx.doi.org/10.54097/hset.v31i.5152.

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A random walk is known as a process that a random walker makes consecutive steps in space at equal intervals of time and the length and direction of each step is determined independently. It is an example of Markov processes, meaning that future movements of the random walker are independent of the past. The applications of random walks are quite popular in the field of mathematics, probability and computer science. Random walk related models can be used in different areas such as prediction, recommendation algorithm to recent supervised learning and networks. It is noticeable that there are f

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9

GUILLOTIN-PLANTARD, NADINE, and RENÉ SCHOTT. "DYNAMIC QUANTUM BERNOULLI RANDOM WALKS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, no. 02 (2008): 213–29. http://dx.doi.org/10.1142/s021902570800304x.

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Quantum Bernoulli random walks can be realized as random walks on the dual of SU(2). We use this realization in order to study a model of dynamic quantum Bernoulli random walk with time-dependent transitions. For the corresponding dynamic random walk on the dual of SU(2), we prove several limit theorems (local limit theorem, central limit theorem, law of large numbers, large deviation principle). In addition, we characterize a large class of transient dynamic random walks.

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10

Roichman, Yuval. "On random random walks." Annals of Probability 24, no. 2 (1996): 1001–11. http://dx.doi.org/10.1214/aop/1039639375.

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11

Nogués, J., J. L. Costa-Krämer, and K. V. Rao. "Are random walks random?" Physica A: Statistical Mechanics and its Applications 250, no. 1-4 (1998): 327–34. http://dx.doi.org/10.1016/s0378-4371(97)00540-2.

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12

Randriamaro, Hery. "A determinant formula from random walks." Archivum Mathematicum, no. 5 (2023): 421–31. http://dx.doi.org/10.5817/am2023-5-421.

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13

Liu, Jiachen. "The Recurrence and Transience of Random Walks." Highlights in Science, Engineering and Technology 94 (April 26, 2024): 431–36. http://dx.doi.org/10.54097/mdb42w42.

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This article reviews the research history and application fields of random walks and abstracts random walks into a time-homogeneous Markov chain to study their recurrent and transient properties. For one-dimensional and two-dimensional random walks, the likelihood of returning in steps and the probability of returning for the first time in steps of each state are first introduced, along with their relationship. Then the Stirling's formula is given, which is utilized to estimate the probability of returning in n steps, and the convergence and divergence of infinite series is used to prove that

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14

Oluwarotimi Israel Oluwafemi, Emmanuel Olamigoke Famakinwa, and Ometere Deborah Balogun. "Random walk theory and application." World Journal of Advanced Engineering Technology and Sciences 11, no. 2 (2024): 346–67. http://dx.doi.org/10.30574/wjaets.2024.11.2.0116.

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This project presents an overview of Random Walk Theory and its applications, as discussed in the provided project work. Random Walk Theory posits that changes in elements like stock prices follow a distribution independent of past movements, making future predictions challenging. Originating from the work of French mathematician Louis Bachelier and later popularized by economist Burton Markiel, the theory finds extensive applications beyond finance, spanning fields such as psychology, economics, and physics. The project delves into various types of random walks, including symmetric random wal

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15

Rabinovich, Savely, H. Eduardo Roman, Shlomo Havlin, and Armin Bunde. "Critical dimensions for random walks on random-walk chains." Physical Review E 54, no. 4 (1996): 3606–8. http://dx.doi.org/10.1103/physreve.54.3606.

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16

Zifferer, Gerhard, and Oskar Friedrich Olaj. "Shape asymmetry of random walks and nonreversal random walks." Journal of Chemical Physics 100, no. 1 (1994): 636–39. http://dx.doi.org/10.1063/1.466926.

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17

Jing, Xing-Li, Xiang Ling, Jiancheng Long, Qing Shi, and Mao-Bin Hu. "Mean first return time for random walks on weighted networks." International Journal of Modern Physics C 26, no. 06 (2015): 1550068. http://dx.doi.org/10.1142/s0129183115500680.

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Random walks on complex networks are of great importance to understand various types of phenomena in real world. In this paper, two types of biased random walks on nonassortative weighted networks are studied: edge-weight-based random walks and node-strength-based random walks, both of which are extended from the normal random walk model. Exact expressions for stationary distribution and mean first return time (MFRT) are derived and examined by simulation. The results will be helpful for understanding the influences of weights on the behavior of random walks.

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18

Papadias, Serafeim, Zoi Kaoudi, Jorge-Arnulfo Quiané-Ruiz, and Volker Markl. "Space-efficient random walks on streaming graphs." Proceedings of the VLDB Endowment 16, no. 2 (2022): 356–68. http://dx.doi.org/10.14778/3565816.3565835.

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Graphs in many applications, such as social networks and IoT, are inherently streaming, involving continuous additions and deletions of vertices and edges at high rates. Constructing random walks in a graph, i.e., sequences of vertices selected with a specific probability distribution, is a prominent task in many of these graph applications as well as machine learning (ML) on graph-structured data. In a streaming scenario, random walks need to constantly keep up with the graph updates to avoid stale walks and thus, performance degradation in the downstream tasks. We present Wharf, a system tha

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19

Bellaachia, Abdelghani, and Mohammed Al-Dhelaan. "Random Walks in Hypergraph." International Journal of Education and Information Technologies 15 (March 10, 2021): 13–20. http://dx.doi.org/10.46300/9109.2021.15.2.

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Random walks on graphs have been extensively used for a variety of graph-based problems such as ranking vertices, predicting links, recommendations, and clustering. However, many complex problems mandate a high-order graph representation to accurately capture the relationship structure inherent in them. Hypergraphs are particularly useful for such models due to the density of information stored in their structure. In this paper, we propose a novel extension to defining random walks on hypergraphs. Our proposed approach combines the weights of destination vertices and hyperedges in a probabilis

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20

Forrester, P. J. "Random walks and random permutations." Journal of Physics A: Mathematical and General 34, no. 31 (2001): L417—L423. http://dx.doi.org/10.1088/0305-4470/34/31/101.

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21

Zeitouni, Ofer. "Random walks in random environments." Journal of Physics A: Mathematical and General 39, no. 40 (2006): R433—R464. http://dx.doi.org/10.1088/0305-4470/39/40/r01.

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22

INUI, NORIO, YOSHINAO KONISHI, NORIO KONNO, and TAKAHIRO SOSHI. "FLUCTUATIONS OF QUANTUM RANDOM WALKS ON CIRCLES." International Journal of Quantum Information 03, no. 03 (2005): 535–49. http://dx.doi.org/10.1142/s0219749905001079.

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Temporal fluctuations in the Hadamard walk on circles are studied. A temporal standard deviation of probability that a quantum random walker is positive at a given site is introduced to manifest striking differences between quantum and classical random walks. An analytical expression of the temporal standard deviation on a circle with odd sites is shown and its asymptotic behavior is considered for large system size. In contrast with classical random walks, the temporal fluctuation of quantum random walks depends on the position and initial conditions, since temporal standard deviation of the

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23

Rosenthal, Jeffrey S. "Random walks on discrete and continuous circles." Journal of Applied Probability 30, no. 4 (1993): 780–89. http://dx.doi.org/10.2307/3214512.

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We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the ‘generation gap' process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the continuous circle S1.

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24

Rosenthal, Jeffrey S. "Random walks on discrete and continuous circles." Journal of Applied Probability 30, no. 04 (1993): 780–89. http://dx.doi.org/10.1017/s0021900200044569.

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We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the ‘generation gap' process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the continuous circle S 1.

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25

Pato, Mauricio P. "Disordered Random Walks." Brazilian Journal of Physics 51, no. 2 (2021): 238–43. http://dx.doi.org/10.1007/s13538-020-00818-y.

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26

Chiappori, P. A., and R. Guesnerie. "Rational Random Walks." Review of Economic Studies 60, no. 4 (1993): 837–64. http://dx.doi.org/10.2307/2298102.

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27

Letac, Gérard, and Mauro Piccioni. "Dirichlet Random Walks." Journal of Applied Probability 51, no. 4 (2014): 1081–99. http://dx.doi.org/10.1239/jap/1421763329.

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This paper provides tools for the study of the Dirichlet random walk in Rd. We compute explicitly, for a number of cases, the distribution of the random variable W using a form of Stieltjes transform of W instead of the Laplace transform, replacing the Bessel functions with hypergeometric functions. This enables us to simplify some existing results, in particular, some of the proofs by Le Caër (2010), (2011). We extend our results to the study of the limits of the Dirichlet random walk when the number of added terms goes to ∞, interpreting the results in terms of an integral by a Dirichlet pro

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28

SUBRAMANI, K. "CASCADING RANDOM WALKS." International Journal of Foundations of Computer Science 16, no. 03 (2005): 599–622. http://dx.doi.org/10.1142/s0129054105003182.

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In this paper, we discuss a simple, Monte Carlo algorithm for the problem of checking whether a Quantified Boolean Formula (QBF) in Conjunctive Normal Form (CNF), with at most two literals per clause has a model. The term k-CNF is used to describe boolean formulas in CNF, with at most k literals per clause and the problem of checking whether a given k-CNF formula is satisfiable is called the k-SAT problem. A QBF is a boolean formula, accompanied by a quantifier string which imposes a linear ordering on the variables of that formula. The problem of finding a model for a QBF formula in CNF, with

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29

Aharonov, Y., L. Davidovich, and N. Zagury. "Quantum random walks." Physical Review A 48, no. 2 (1993): 1687–90. http://dx.doi.org/10.1103/physreva.48.1687.

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30

Das Sarma, Atish, Danupon Nanongkai, Gopal Pandurangan, and Prasad Tetali. "Distributed Random Walks." Journal of the ACM 60, no. 1 (2013): 1–31. http://dx.doi.org/10.1145/2432622.2432624.

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31

Collevecchio, Andrea, Kais Hamza, and Meng Shi. "Bootstrap random walks." Stochastic Processes and their Applications 126, no. 6 (2016): 1744–60. http://dx.doi.org/10.1016/j.spa.2015.11.016.

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32

Letac, Gérard, and Mauro Piccioni. "Dirichlet Random Walks." Journal of Applied Probability 51, no. 04 (2014): 1081–99. http://dx.doi.org/10.1017/s0021900200011992.

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This paper provides tools for the study of the Dirichlet random walk inRd. We compute explicitly, for a number of cases, the distribution of the random variableWusing a form of Stieltjes transform ofWinstead of the Laplace transform, replacing the Bessel functions with hypergeometric functions. This enables us to simplify some existing results, in particular, some of the proofs by Le Caër (2010), (2011). We extend our results to the study of the limits of the Dirichlet random walk when the number of added terms goes to ∞, interpreting the results in terms of an integral by a Dirichlet process.

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33

Addario-Berry, L., H. Cairns, L. Devroye, C. Kerriou, and R. Mitchell. "Hipster random walks." Probability Theory and Related Fields 178, no. 1-2 (2020): 437–73. http://dx.doi.org/10.1007/s00440-020-00980-z.

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34

Filk, Thomas. "Noncommutative random walks." Nuclear Physics B - Proceedings Supplements 20 (May 1991): 762–65. http://dx.doi.org/10.1016/0920-5632(91)91017-e.

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35

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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36

Eichelsbacher, Peter, and Wolfgang König. "Ordered Random Walks." Electronic Journal of Probability 13 (2008): 1307–36. http://dx.doi.org/10.1214/ejp.v13-539.

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37

Ohira, Toru, and John G. Milton. "Delayed random walks." Physical Review E 52, no. 3 (1995): 3277–80. http://dx.doi.org/10.1103/physreve.52.3277.

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38

Aslangul, Claude. "Multiplicative random walks." Physica A: Statistical Mechanics and its Applications 215, no. 4 (1995): 495–510. http://dx.doi.org/10.1016/0378-4371(95)00003-p.

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39

Azar, Yossi, Andrei Z. Broder, Anna R. Karlin, Nathan Linial, and Steven Phillips. "Biased random walks." Combinatorica 16, no. 1 (1996): 1–18. http://dx.doi.org/10.1007/bf01300124.

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40

de la Selva, S. M. T., Katja Lindenberg, and Bruce J. West. "Correlated random walks." Journal of Statistical Physics 53, no. 1-2 (1988): 203–19. http://dx.doi.org/10.1007/bf01011553.

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41

Luzia, Nuno. "Quantitative recurrence results for random walks." Stochastics and Dynamics 18, no. 03 (2018): 1850003. http://dx.doi.org/10.1142/s021949371850003x.

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First, we prove an almost sure local central limit theorem for lattice random walks in the plane. The corresponding version for random walks in the line has been considered previously by the author. This gives us an extension of Pólya’s Recurrence Theorem, namely we consider an appropriate subsequence of the random walk and give the asymptotic number of returns to the origin and other states. Secondly, we prove an almost sure local central limit theorem for (not necessarily lattice) random walks in the line or in the plane, which will also give us quantitative recurrence results. Finally, we p

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42

Mc Gettrick, M. "One dimensional quantum walks with memory." Quantum Information and Computation 10, no. 5&6 (2010): 509–24. http://dx.doi.org/10.26421/qic10.5-6-9.

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We investigate the quantum versions of a one-dimensional random walk, whose corresponding Markov Chain is of order 2. This corresponds to the walk having a memory of one previous step. We derive the amplitudes and probabilities for these walks, and point out how they differ from both classical random walks, and quantum walks without memory.

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43

YANG, ZHIHUI. "LARGE DEVIATION ASYMPTOTICS FOR RANDOM-WALK TYPE PERTURBATIONS." Stochastics and Dynamics 07, no. 01 (2007): 75–89. http://dx.doi.org/10.1142/s0219493707001950.

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Symmetric random walks can be arranged to converge to a Wiener process in the area of normal deviation. However, random walks and Wiener processes have, in general, different asymptotics of the large deviation probabilities. The action functionals for random-walks and Wiener processes are compared in this paper. The correction term is calculated. Exit problem and stochastic resonance for random-walk-type perturbation are also considered and compared with the white-noise-type perturbation.

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44

Nicolau, João. "STATIONARY PROCESSES THAT LOOK LIKE RANDOM WALKS— THE BOUNDED RANDOM WALK PROCESS IN DISCRETE AND CONTINUOUS TIME." Econometric Theory 18, no. 1 (2002): 99–118. http://dx.doi.org/10.1017/s0266466602181060.

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Several economic and financial time series are bounded by an upper and lower finite limit (e.g., interest rates). It is not possible to say that these time series are random walks because random walks are limitless with probability one (as time goes to infinity). Yet, some of these time series behave just like random walks. In this paper we propose a new approach that takes into account these ideas. We propose a discrete-time and a continuous-time process (diffusion process) that generate bounded random walks. These paths are almost indistinguishable from random walks, although they are stocha

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45

Yang, Yufei. "Principle and application of random walk simulation: Multilayer networks, predation and stock market." Theoretical and Natural Science 13, no. 1 (2023): 36–44. http://dx.doi.org/10.54254/2753-8818/13/20240771.

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Given the probabilities (which remain unchanged at each step) of travelling a certain distance in a certain direction, a random walk is a method used in probability theory to determine the likely position of a point depending on random movements. Markov processes, in which future behavior is independent of previous behavior, include random walks as an illustration. This study will mainly pay attention to three different applications of random walks in aspects of multilayer networks, predation and stock market. A real and intricate network could be solved by a mathematical equation depending on

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46

Berger, Quentin, Celine Bonnet, Lucile Laulin, and Kilian Raschel. "Some topics in random walks." ESAIM: Proceedings and Surveys 80 (2025): 51–71. https://doi.org/10.1051/proc/202580051.

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We collect a few recent results on random walks, which are ubiquitous in probability theory. The topics covered are: persistence problems for stochastic processes, large fluctuations in multi-scale modeling for rest hematopoiesis, and fine properties of the elephant random walk.

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47

Li, Yuqiang. "Moderate Deviations for Stable Random Walks in Random Scenery." Journal of Applied Probability 49, no. 1 (2012): 280–94. http://dx.doi.org/10.1239/jap/1331216847.

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In this paper, a moderate deviation theorem for one-dimensional stable random walks in random scenery is proved. The proof relies on the analysis of maximum local times of stable random walks, and the comparison of moments between random walks in random scenery and self-intersection local times of the underlying random walks.

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48

Li, Yuqiang. "Moderate Deviations for Stable Random Walks in Random Scenery." Journal of Applied Probability 49, no. 01 (2012): 280–94. http://dx.doi.org/10.1017/s0021900200008998.

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In this paper, a moderate deviation theorem for one-dimensional stable random walks in random scenery is proved. The proof relies on the analysis of maximum local times of stable random walks, and the comparison of moments between random walks in random scenery and self-intersection local times of the underlying random walks.

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49

GREENHALGH, ANDREW S. "A Model for Random Random-Walks on Finite Groups." Combinatorics, Probability and Computing 6, no. 1 (1997): 49–56. http://dx.doi.org/10.1017/s096354839600257x.

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A model for a random random-walk on a finite group is developed where the group elements that generate the random-walk are chosen uniformly and with replacement from the group. When the group is the d-cube Zd2, it is shown that if the generating set is size k then as d → ∞ with k − d → ∞ almost all of the random-walks converge to uniform in k ln (k/(k − d))/4+ρk steps, where ρ is any constant satisfying ρ > −ln (ln 2)/4.

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50

Gut, Allan, and Ulrich Stadtmüller. "Elephant random walks: A review." Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, no. 54 (2023): 171–98. https://doi.org/10.71352/ac.54.171.

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In the simple random walk the steps are independent, whereas in the elephant random walk (ERW), which was introduced by Schütz and Trimper in 2004 [33], the next step always depends on the whole path so far. In a series of earlier papers we have investigated some variations and extensions, in particular cases when the elephant has a restricted memory. In the present paper we summarize and extend some results on elephant random walks, closing with some remarks and open questions.

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