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Journal articles on the topic 'Random walk'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 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

Van Doorn, Erik A., and Pauline Schrijner. "Random walk polynomials and random walk measures." Journal of Computational and Applied Mathematics 49, no. 1-3 (1993): 289–96. http://dx.doi.org/10.1016/0377-0427(93)90162-5.

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3

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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4

Tran, Loc Hoang, Linh Hoang Tran, Hoang Trang, and Le Trung Hieu. "Combinatorial and Random Walk Hypergraph Laplacian EigenmapsCombinatorial and Random Walk Hypergraph Laplacian Eigenmaps." International Journal of Machine Learning and Computing 5, no. 6 (2015): 462–66. http://dx.doi.org/10.18178/ijmlc.2015.5.6.553.

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5

Mundy, John N. "Random Walk." Defect and Diffusion Forum 353 (May 2014): 1–7. http://dx.doi.org/10.4028/www.scientific.net/ddf.353.1.

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Random walk is the central concept in the mathematical formalization of the diffusion coefficient and so when asked a year ago to present a talk at a diffusion conference it appeared to be a totally appropriate topic. I spent most of my career studying diffusion and even after twenty years in retirement I believed I could write an interesting story about the importance of random walk to diffusion. Unfortunately when I sat down to write I discovered two problems: in the majority of materials that I investigated atoms did follow a random walk; and the history of random walk has been well documen

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6

Butler, Mary Odell. "Random Walk." NAPA Bulletin 26, no. 1 (2008): 20–31. http://dx.doi.org/10.1525/napa.2006.26.1.20.

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7

van der Hofstad, Remco, Tim Hulshof, and Jan Nagel. "Random walk on barely supercritical branching random walk." Probability Theory and Related Fields 177, no. 1-2 (2019): 1–53. http://dx.doi.org/10.1007/s00440-019-00942-0.

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8

Croydon, David A. "Random Walk on the Range of Random Walk." Journal of Statistical Physics 136, no. 2 (2009): 349–72. http://dx.doi.org/10.1007/s10955-009-9785-2.

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9

Kutner, R. "Biased random walk on a biased random walk." Physica A: Statistical Mechanics and its Applications 171, no. 1 (1991): 43–46. http://dx.doi.org/10.1016/0378-4371(91)90356-h.

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10

He, Yitong. "Beyond Polya’S Random Walk Theorem." Highlights in Science, Engineering and Technology 88 (March 29, 2024): 149–55. http://dx.doi.org/10.54097/jw2bp960.

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A random walk can be regarded as a probability model depicting some degree of randomness, which has lots of interdisciplinary applications in physics, biochemistry and computer science. In this paper, the recurrence classifications of five different random walk models are presented along with their relevant studies. In order to explore the essential reasons leading to the qualitative change of simple random walks’ recurrence property, the classification results of the five simple random walk variants are horizontally discussed. As a result, a positive bias is found to be the denominator shared

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11

Pandey, R. B. "Anomalous conformation of polymer chains: random walk of a random walk on a random walk." Journal of Physics A: Mathematical and General 19, no. 2 (1986): L53—L56. http://dx.doi.org/10.1088/0305-4470/19/2/006.

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12

KOJIMA, Seiji, Tomoko MASAIKE, Tohru MINAMINO, and Makoto MIYATA. "Following the Random Walk." Seibutsu Butsuri 54, no. 4 (2014): 226–29. http://dx.doi.org/10.2142/biophys.54.226.

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13

Amir, Gideon, Itai Benjamini, and Gady Kozma. "Excited random walk against a wall." Probability Theory and Related Fields 140, no. 1-2 (2007): 83–102. http://dx.doi.org/10.1007/s00440-007-0058-1.

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14

LI, KEQIN. "PERFORMANCE ANALYSIS AND EVALUATION OF RANDOM WALK ALGORITHMS ON WIRELESS NETWORKS." International Journal of Foundations of Computer Science 23, no. 04 (2012): 779–802. http://dx.doi.org/10.1142/s0129054112400369.

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We propose a model of dynamically evolving random networks and give an analytical result of the cover time of the simple random walk algorithm on a dynamic random symmetric planar point graph. Our dynamic network model considers random node distribution and random node mobility. We analyze the cover time of the parallel random walk algorithm on a complete network and show by numerical data that k parallel random walks reduce the cover time by almost a factor of k. We present simulation results for four random walk algorithms on random asymmetric planar point graphs. These algorithms include th

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15

Mallein, Bastien, and Piotr Miłoś. "Brownian motion and random walk above quenched random wall." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 54, no. 4 (2018): 1877–916. http://dx.doi.org/10.1214/17-aihp859.

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16

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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17

Deng, Youjin, Timothy M. Garoni, Jens Grimm, and Zongzheng Zhou. "Two-point functions of random-length random walk on high-dimensional boxes." Journal of Statistical Mechanics: Theory and Experiment 2024, no. 2 (2024): 023203. http://dx.doi.org/10.1088/1742-5468/ad13fb.

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Abstract We study the two-point functions of a general class of random-length random walks (RLRWs) on finite boxes in Z d with d ⩾ 3 , and provide precise asymptotics for their behaviour. We show that in a finite box of side length L, the two-point function is asymptotic to the infinite-lattice two-point function when the typical walk length is o ( L 2 ) , but develops a plateau when the typical walk length is Ω ( L 2 ) . We also numerically study walk length moments and limiting distributions of the self-avoiding walk and Ising model on five-dimensional tori, and find that they agree asymptot

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18

Kang, Yuanbao, and Caishi Wang. "Quantum random walk polynomial and quantum random walk measure." Quantum Information Processing 13, no. 5 (2014): 1191–209. http://dx.doi.org/10.1007/s11128-013-0724-4.

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19

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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20

De Coninck, Joël, François Dunlop, and Thierry Huillet. "Random walk versus random line." Physica A: Statistical Mechanics and its Applications 388, no. 19 (2009): 4034–40. http://dx.doi.org/10.1016/j.physa.2009.06.030.

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21

Gromov, M. "Random walk in random groups." Geometric and Functional Analysis 13, no. 1 (2003): 73–146. http://dx.doi.org/10.1007/s000390300002.

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22

GRAMATOVICI, Sorina, and Corina-Mihaela MORTICI. "RANDOM WALK HYPOTHESIS ON BUCHAREST STOCK EXCHANGE." Review of the Air Force Academy 16, no. 2 (2018): 59–74. http://dx.doi.org/10.19062/1842-9238.2018.16.2.7.

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23

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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24

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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25

Dshalalow, Jewgeni H., and Ryan T. White. "Current Trends in Random Walks on Random Lattices." Mathematics 9, no. 10 (2021): 1148. http://dx.doi.org/10.3390/math9101148.

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In a classical random walk model, a walker moves through a deterministic d-dimensional integer lattice in one step at a time, without drifting in any direction. In a more advanced setting, a walker randomly moves over a randomly configured (non equidistant) lattice jumping a random number of steps. In some further variants, there is a limited access walker’s moves. That is, the walker’s movements are not available in real time. Instead, the observations are limited to some random epochs resulting in a delayed information about the real-time position of the walker, its escape time, and location

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26

Codling, Edward A., Michael J. Plank, and Simon Benhamou. "Random walk models in biology." Journal of The Royal Society Interface 5, no. 25 (2008): 813–34. http://dx.doi.org/10.1098/rsif.2008.0014.

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Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on the extensions of simple random walk processes. In this review paper, our aim is twofold: to introduce the mathematics behind random walks in a straightforward manner and to explain how such models can be used to aid our understanding of biological processes. We introduce the mathematical theory behind the simple random walk and explain how this relates to Brownian

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27

Powell, Elisabeth. "A Random Walk." Journal of Business Anthropology 9, no. 2 (2020): 406–25. http://dx.doi.org/10.22439/jba.v9i2.6133.

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28

Haw, Mark. "Einstein's random walk." Physics World 18, no. 1 (2005): 19–22. http://dx.doi.org/10.1088/2058-7058/18/1/25.

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29

Orlin, Ben. "A random walk." Math Horizons 26, no. 2 (2018): 17. http://dx.doi.org/10.1080/10724117.2018.1535680.

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30

Luque, Bartolo, and Fernando J. Ballesteros. "Random walk networks." Physica A: Statistical Mechanics and its Applications 342, no. 1-2 (2004): 207–13. http://dx.doi.org/10.1016/j.physa.2004.04.080.

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31

Engländer, János, and Stanislav Volkov. "Impatient Random Walk." Journal of Theoretical Probability 32, no. 4 (2019): 2020–43. http://dx.doi.org/10.1007/s10959-019-00901-4.

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32

Frolov, S. I. "Brownian Random Walk." Journal of Mathematical Sciences 221, no. 4 (2017): 522–29. http://dx.doi.org/10.1007/s10958-017-3247-1.

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33

ORENSHTEIN, TAL, and IGOR SHINKAR. "Greedy Random Walk." Combinatorics, Probability and Computing 23, no. 2 (2013): 269–89. http://dx.doi.org/10.1017/s0963548313000552.

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We study a discrete time self-interacting random process on graphs, which we call greedy random walk. The walker is located initially at some vertex. As time evolves, each vertex maintains the set of adjacent edges touching it that have not yet been crossed by the walker. At each step, the walker, being at some vertex, picks an adjacent edge among the edges that have not traversed thus far according to some (deterministic or randomized) rule. If all the adjacent edges have already been traversed, then an adjacent edge is chosen uniformly at random. After picking an edge the walker jumps along

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34

Benjamini, Itai, and David Wilson. "Excited Random Walk." Electronic Communications in Probability 8 (2003): 86–92. http://dx.doi.org/10.1214/ecp.v8-1072.

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35

Turban, L. "Iterated random walk." Europhysics Letters (EPL) 65, no. 5 (2004): 627–32. http://dx.doi.org/10.1209/epl/i2003-10165-4.

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36

Davis, Burgess. "Reinforced random walk." Probability Theory and Related Fields 84, no. 2 (1990): 203–29. http://dx.doi.org/10.1007/bf01197845.

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37

Brewer, Neil. "Random Walk Models." Applied Cognitive Psychology 26, no. 1 (2011): 164–65. http://dx.doi.org/10.1002/acp.1820.

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38

Brown, Eric. "A Non-Random Walk Down Wall Street." Journal of Economic Surveys 13, no. 4 (1999): 477–78. http://dx.doi.org/10.1111/1467-6419.00091.

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39

De Coninck, Joël, François Dunlop, and Thierry Huillet. "Random Walk Weakly Attracted to a Wall." Journal of Statistical Physics 133, no. 2 (2008): 271–80. http://dx.doi.org/10.1007/s10955-008-9609-9.

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40

Bulkley, George. "A Non‐Random Walk Down Wall Street." Economic Journal 113, no. 491 (2003): F668—F670. http://dx.doi.org/10.1046/j.0013-0133.2003.172_9.x.

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41

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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42

Zerner, Martin P. W. "multidimensional random walk in random environment." Annals of Probability 26, no. 4 (1998): 1446–76. http://dx.doi.org/10.1214/aop/1022855870.

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43

Sinai, Ya G. "A Random Walk with Random Potential." Theory of Probability & Its Applications 38, no. 2 (1994): 382–85. http://dx.doi.org/10.1137/1138036.

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44

Bordenave, Charles, Pietro Caputo, and Justin Salez. "Random walk on sparse random digraphs." Probability Theory and Related Fields 170, no. 3-4 (2017): 933–60. http://dx.doi.org/10.1007/s00440-017-0796-7.

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45

Björnberg, Jakob E., and Sigurdur Örn Stefánsson. "Random Walk on Random Infinite Looptrees." Journal of Statistical Physics 158, no. 6 (2015): 1234–61. http://dx.doi.org/10.1007/s10955-014-1174-9.

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46

James, J. Kung, and Lin Wen-Ying. "How has the Chinese Yuan Evolved since the 2005 Reform?" Journal of Economics and Business 2, no. 3 (2019): 855–62. https://doi.org/10.31014/aior.1992.02.03.132.

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This study employs the bootstrap method to explore the evolution of the Chinese yuan. We use the following three random walks to characterize the evolution of the yuan: an IID-parameterized random walk, an ARCH(3)-parameterized random walk, and a GARCH(1,1)-parameterized random walk. To proceed, we use the bootstrap method to generate 10,000 artificial yuan series from each random walk and compute the return from the trading rule (i.e., moving average or trading range break) for each of the 10,000 artificial yuan series. Then, we construct a 95% percentile interval with these 10,000 returns to

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47

Lawler, G. F. "Loop-erased self-avoiding random walk and the Laplacian random walk." Journal of Physics A: Mathematical and General 20, no. 13 (1987): 4565–68. http://dx.doi.org/10.1088/0305-4470/20/13/056.

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48

XU, BAOMIN, TINGLIN XIN, YUNFENG WANG, and YANPIN ZHAO. "LOCAL RANDOM WALK WITH DISTANCE MEASURE." Modern Physics Letters B 27, no. 08 (2013): 1350055. http://dx.doi.org/10.1142/s0217984913500553.

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Link prediction based on random walks has been widely used. The existing random walk algorithms ignore the probability of a walker visit from the initial node to the destination node for the first time, which makes a major contribution to establish links in some networks. To deal with the problem, we develop a link prediction method named Local Random Walk with Distance (LRWD) based on local random walk and the shortest distance of node pairs. In LRWD, walkers walk with their own steps rather than uniform steps. To evaluate the performance of the LRWD algorithm, we present the concept of dista

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49

Fang, Xiao, Han L. Gan, Susan Holmes, et al. "Arcsine laws for random walks generated from random permutations with applications to genomics." Journal of Applied Probability 58, no. 4 (2021): 851–67. http://dx.doi.org/10.1017/jpr.2021.14.

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AbstractA classical result for the simple symmetric random walk with 2n steps is that the number of steps above the origin, the time of the last visit to the origin, and the time of the maximum height all have exactly the same distribution and converge when scaled to the arcsine law. Motivated by applications in genomics, we study the distributions of these statistics for the non-Markovian random walk generated from the ascents and descents of a uniform random permutation and a Mallows(q) permutation and show that they have the same asymptotic distributions as for the simple random walk. We al

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50

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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