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Journal articles on the topic 'Random walk'

Author: Grafiati

Published: 4 June 2021

Last updated: 21 September 2024

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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 (August 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 (December 1993): 289–96. http://dx.doi.org/10.1016/0377-0427(93)90162-5.

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3

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 (December 2015): 462–66. http://dx.doi.org/10.18178/ijmlc.2015.5.6.553.

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4

Boissard, Emmanuel, Serge Cohen, Thibault Espinasse, and James Norris. "Diffusivity of a random walk on random walks." Random Structures & Algorithms 47, no. 2 (April 16, 2014): 267–83. http://dx.doi.org/10.1002/rsa.20541.

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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 documented and shows little connection to diffusion. The phrase was coined in 1905 at a time of rapid changes in physics. Scientists are not accustomed to writing history and as Henry Ford said around the same period of time “History is bunk”. He also remarked, "You can have any color (car) as long as it's black". This essay presents my story (not his- or her- tory) of why the use of the phrase random walk in discussions of diffusion in solids is also bunk.

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6

Butler, Mary Odell. "Random Walk." NAPA Bulletin 26, no. 1 (January 8, 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 (September 25, 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 (July 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 (February 1991): 43–46. http://dx.doi.org/10.1016/0378-4371(91)90356-h.

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10

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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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 (February 1, 1986): L53—L56. http://dx.doi.org/10.1088/0305-4470/19/2/006.

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12

Amir, Gideon, Itai Benjamini, and Gady Kozma. "Excited random walk against a wall." Probability Theory and Related Fields 140, no. 1-2 (February 15, 2007): 83–102. http://dx.doi.org/10.1007/s00440-007-0058-1.

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13

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 (November 2018): 1877–916. http://dx.doi.org/10.1214/17-aihp859.

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14

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 (October 1, 1996): 3606–8. http://dx.doi.org/10.1103/physreve.54.3606.

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15

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 by random walk variants whose recurrence classifications are different from that of simple random walks. A limited walking direction is also found useful in reversing the recurrence result. Besides answering the qualitative change question, this paper is also dedicated to provide a summary of the recurrence properties of different current random walk models, in order to help researchers in related fields to quickly get the picture of some random walk models.

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16

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

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17

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 (April 30, 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 walks, and explores their implications in different spaces, from graphs to higher-dimensional vector spaces. It provides definitions, examples, and graphical representations to elucidate random walk concepts, highlighting their relevance in practical scenarios like particle movement and stock price fluctuations. Key concepts such as the reflection principle and the main lemma are discussed to provide a comprehensive understanding of random walks and their properties. Through examples and lemmas, the project elucidates the mathematical foundations of random walks, offering insights into their behavior and applications across diverse disciplines. In summary, this project contributes to a deeper comprehension of Random Walk Theory, serving as a fundamental framework for understanding stochastic processes and their real-world implications.

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18

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 (February 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 asymptotically with the known results for the self-avoiding walk on the complete graph, both at the critical point and also for a broad class of scaling windows/pseudocritical points. Furthermore, we show that the two-point function of the finite-box RLRW, with walk length chosen via the complete graph self-avoiding walk, agrees numerically with the two-point functions of the self-avoiding walk and Ising model on five-dimensional tori. We conjecture that these observations in five dimensions should also hold in all higher dimensions.

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19

GRAMATOVICI, Sorina, and Corina-Mihaela MORTICI. "RANDOM WALK HYPOTHESIS ON BUCHAREST STOCK EXCHANGE." Review of the Air Force Academy 16, no. 2 (October 31, 2018): 59–74. http://dx.doi.org/10.19062/1842-9238.2018.16.2.7.

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20

LI, KEQIN. "PERFORMANCE ANALYSIS AND EVALUATION OF RANDOM WALK ALGORITHMS ON WIRELESS NETWORKS." International Journal of Foundations of Computer Science 23, no. 04 (June 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 the simple random walk algorithm, the intelligent random walk algorithm, the parallel random walk algorithm, and the parallel intelligent random walk algorithm. Our random network model considers random node distribution and random battery transmission power. Performance measures include normalized cover time, probability distribution of the length of random walks, and load distribution.

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21

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

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22

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

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23

Powell, Elisabeth. "A Random Walk." Journal of Business Anthropology 9, no. 2 (November 30, 2020): 406–25. http://dx.doi.org/10.22439/jba.v9i2.6133.

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24

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

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25

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

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26

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

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27

Engländer, János, and Stanislav Volkov. "Impatient Random Walk." Journal of Theoretical Probability 32, no. 4 (April 16, 2019): 2020–43. http://dx.doi.org/10.1007/s10959-019-00901-4.

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28

Frolov, S. I. "Brownian Random Walk." Journal of Mathematical Sciences 221, no. 4 (January 28, 2017): 522–29. http://dx.doi.org/10.1007/s10958-017-3247-1.

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29

ORENSHTEIN, TAL, and IGOR SHINKAR. "Greedy Random Walk." Combinatorics, Probability and Computing 23, no. 2 (November 20, 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 it to the neighbouring vertex. We show that the expected edge cover time of the greedy random walk is linear in the number of edges for certain natural families of graphs. Examples of such graphs include the complete graph, even degree expanders of logarithmic girth, and the hypercube graph. We also show that GRW is transient in$\mathbb{Z}^d$for alld≥ 3.

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30

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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31

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

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32

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

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33

Brewer, Neil. "Random Walk Models." Applied Cognitive Psychology 26, no. 1 (July 22, 2011): 164–65. http://dx.doi.org/10.1002/acp.1820.

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34

GREENHALGH, ANDREW S. "A Model for Random Random-Walks on Finite Groups." Combinatorics, Probability and Computing 6, no. 1 (March 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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35

Dshalalow, Jewgeni H., and Ryan T. White. "Current Trends in Random Walks on Random Lattices." Mathematics 9, no. 10 (May 19, 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 outside a bounded subset of the real space. In this case we target the virtual first passage (or escape) time. Thus, unlike standard random walk problems, rather than crossing the boundary, we deal with the walker’s escape location arbitrarily distant from the boundary. In this paper, we give a short historical background on random walk, discuss various directions in the development of random walk theory, and survey most of our results obtained in the last 25–30 years, including the very recent ones dated 2020–21. Among different applications of such random walks, we discuss stock markets, stochastic networks, games, and queueing.

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36

Codling, Edward A., Michael J. Plank, and Simon Benhamou. "Random walk models in biology." Journal of The Royal Society Interface 5, no. 25 (April 15, 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 motion and diffusive processes in general. We demonstrate how these simple models can be extended to include drift and waiting times or be used to calculate first passage times. We discuss biased random walks and show how hyperbolic models can be used to generate correlated random walks. We cover two main applications of the random walk model. Firstly, we review models and results relating to the movement, dispersal and population redistribution of animals and micro-organisms. This includes direct calculation of mean squared displacement, mean dispersal distance, tortuosity measures, as well as possible limitations of these model approaches. Secondly, oriented movement and chemotaxis models are reviewed. General hyperbolic models based on the linear transport equation are introduced and we show how a reinforced random walk can be used to model movement where the individual changes its environment. We discuss the applications of these models in the context of cell migration leading to blood vessel growth (angiogenesis). Finally, we discuss how the various random walk models and approaches are related and the connections that underpin many of the key processes involved.

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37

GUILLOTIN-PLANTARD, NADINE, and RENÉ SCHOTT. "DYNAMIC QUANTUM BERNOULLI RANDOM WALKS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, no. 02 (June 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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38

Brown, Eric. "A Non-Random Walk Down Wall Street." Journal of Economic Surveys 13, no. 4 (September 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 (August 29, 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 (November 1, 2003): F668—F670. http://dx.doi.org/10.1046/j.0013-0133.2003.172_9.x.

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41

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

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42

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

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43

Bordenave, Charles, Pietro Caputo, and Justin Salez. "Random walk on sparse random digraphs." Probability Theory and Related Fields 170, no. 3-4 (August 5, 2017): 933–60. http://dx.doi.org/10.1007/s00440-017-0796-7.

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44

Björnberg, Jakob E., and Sigurdur Örn Stefánsson. "Random Walk on Random Infinite Looptrees." Journal of Statistical Physics 158, no. 6 (January 1, 2015): 1234–61. http://dx.doi.org/10.1007/s10955-014-1174-9.

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45

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 few reviews about randoms for the beginners and how random walks are used nowadays in distinctive areas. Hence, the aim of the article is to provide a brief review of classical random walks, including basic concepts and models of the algorithm and then some applications in the field of computer science for the beginners to understand the significance and future of random walks.

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46

Lawler, G. F. "Loop-erased self-avoiding random walk and the Laplacian random walk." Journal of Physics A: Mathematical and General 20, no. 13 (September 11, 1987): 4565–68. http://dx.doi.org/10.1088/0305-4470/20/13/056.

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47

Steinsaltz, David. "Zeno's walk: A random walk with refinements." Probability Theory and Related Fields 107, no. 1 (January 17, 1997): 99–121. http://dx.doi.org/10.1007/s004400050078.

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48

Huss, Wilfried, Lionel Levine, and Ecaterina Sava-Huss. "Interpolating between random walk and rotor walk." Random Structures & Algorithms 52, no. 2 (November 26, 2017): 263–82. http://dx.doi.org/10.1002/rsa.20747.

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49

XU, BAOMIN, TINGLIN XIN, YUNFENG WANG, and YANPIN ZHAO. "LOCAL RANDOM WALK WITH DISTANCE MEASURE." Modern Physics Letters B 27, no. 08 (March 13, 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 distance distribution. The experimental results show that LRWD can improve the prediction accuracy when the distance distribution of the network is relatively concentrated.

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50

Montero, Miquel. "Random Walks with Invariant Loop Probabilities: Stereographic Random Walks." Entropy 23, no. 6 (June 8, 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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