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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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1

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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2

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

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3

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

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4

Zeitouni, Ofer. "Random walks in random environments." Journal of Physics A: Mathematical and General 39, no. 40 (September 19, 2006): R433—R464. http://dx.doi.org/10.1088/0305-4470/39/40/r01.

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5

Douglas, Jack F. "Random walks and random environments, vol. 2, random environments." Journal of Statistical Physics 87, no. 3-4 (May 1997): 961–62. http://dx.doi.org/10.1007/bf02181260.

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6

Buffet, E., and P. Hannigan. "Directed random walks in random environments." Journal of Statistical Physics 65, no. 3-4 (November 1991): 645–72. http://dx.doi.org/10.1007/bf01053747.

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7

Holmes, Mark, and Thomas S. Salisbury. "Random Walks in Degenerate Random Environments." Canadian Journal of Mathematics 66, no. 5 (October 1, 2014): 1050–77. http://dx.doi.org/10.4153/cjm-2013-017-3.

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Анотація:

AbstractWe study the asymptotic behaviour of random walks in i.i.d. random environments on . The environments need not be elliptic, so some steps may not be available to the random walker. We prove a monotonicity result for the velocity (when it exists) for any 2-valued environment, and show that this does not hold for 3-valued environments without additional assumptions. We give a proof of directional transience and the existence of positive speeds under strong but non-trivial conditions on the distribution of the environment. Our results include generalisations (to the non-elliptic setting) of 0-1 laws for directional transience and, in 2-dimensions, the existence of a deterministic limiting velocity.

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8

Bricmont, J., and A. Kupiainen. "Random walks in asymmetric random environments." Communications in Mathematical Physics 142, no. 2 (December 1991): 345–420. http://dx.doi.org/10.1007/bf02102067.

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9

Shlesinger, Michael F. "Book Review: Random Walks and Random Environments." Fractals 04, no. 01 (March 1996): 111–12. http://dx.doi.org/10.1142/s0218348x96000145.

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10

Lenci, Marco. "Random walks in random environments without ellipticity." Stochastic Processes and their Applications 123, no. 5 (May 2013): 1750–64. http://dx.doi.org/10.1016/j.spa.2013.01.007.

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11

Slade, Gordon. "Book Review: Random walks and random environments." Bulletin of the American Mathematical Society 35, no. 04 (October 1, 1998): 347–50. http://dx.doi.org/10.1090/s0273-0979-98-00762-9.

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12

Scheinhardt, Werner R. W., and Dirk P. Kroese. "A comparison of random walks in dependent random environments." Advances in Applied Probability 48, no. 1 (March 2016): 199–214. http://dx.doi.org/10.1017/apr.2015.13.

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Abstract We provide exact computations for the drift of random walks in dependent random environments, including k-dependent and moving average environments. We show how the drift can be characterized and evaluated using Perron–Frobenius theory. Comparing random walks in various dependent environments, we demonstrate that their drifts can exhibit interesting behavior that depends significantly on the dependency structure of the random environment.

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13

Schulz, M., and S. Stepanow. "Random walks in glasslike environments." Physical Review B 59, no. 21 (June 1, 1999): 13528–30. http://dx.doi.org/10.1103/physrevb.59.13528.

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14

Bunimovich, Leonid A. "Deterministic walks in random environments." Physica D: Nonlinear Phenomena 187, no. 1-4 (January 2004): 20–29. http://dx.doi.org/10.1016/j.physd.2003.09.028.

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15

Majhofer, A., and M. Cieplak. "Non-universality of random walks in random environments." Journal of Physics A: Mathematical and General 21, no. 17 (September 7, 1988): 3481–87. http://dx.doi.org/10.1088/0305-4470/21/17/016.

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16

Alili, S. "Asymptotic behaviour for random walks in random environments." Journal of Applied Probability 36, no. 2 (June 1999): 334–49. http://dx.doi.org/10.1239/jap/1032374457.

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Анотація:

In this paper we consider limit theorems for a random walk in a random environment, (Xn). Known results (recurrence-transience criteria, law of large numbers) in the case of independent environments are naturally extended to the case where the environments are only supposed to be stationary and ergodic. Furthermore, if ‘the fluctuations of the random transition probabilities around are small’, we show that there exists an invariant probability measure for ‘the environments seen from the position of (Xn)’. In the case of uniquely ergodic (therefore non-independent) environments, this measure exists as soon as (Xn) is transient so that the ‘slow diffusion phenomenon’ does not appear as it does in the independent case. Thus, under regularity conditions, we prove that, in this case, the random walk satisfies a central limit theorem for any fixed environment.

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17

Komorowski, T., and S. Olla. "Einstein relation for random walks in random environments." Stochastic Processes and their Applications 115, no. 8 (August 2005): 1279–301. http://dx.doi.org/10.1016/j.spa.2005.03.009.

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18

Alili, S. "Asymptotic behaviour for random walks in random environments." Journal of Applied Probability 36, no. 02 (June 1999): 334–49. http://dx.doi.org/10.1017/s0021900200017174.

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Анотація:

In this paper we consider limit theorems for a random walk in a random environment, (X n ). Known results (recurrence-transience criteria, law of large numbers) in the case of independent environments are naturally extended to the case where the environments are only supposed to be stationary and ergodic. Furthermore, if ‘the fluctuations of the random transition probabilities around are small’, we show that there exists an invariant probability measure for ‘the environments seen from the position of (X n )’. In the case of uniquely ergodic (therefore non-independent) environments, this measure exists as soon as (X n ) is transient so that the ‘slow diffusion phenomenon’ does not appear as it does in the independent case. Thus, under regularity conditions, we prove that, in this case, the random walk satisfies a central limit theorem for any fixed environment.

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19

Horváth, Lajos, and Qi-Man Shao. "Asymptotics for directed random walks in random environments." Acta Mathematica Hungarica 68, no. 1-2 (March 1995): 21–36. http://dx.doi.org/10.1007/bf01874433.

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20

Mardoukhi, Yousof, Jae-Hyung Jeon, Aleksei V. Chechkin, and Ralf Metzler. "Fluctuations of random walks in critical random environments." Physical Chemistry Chemical Physics 20, no. 31 (2018): 20427–38. http://dx.doi.org/10.1039/c8cp03212b.

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Анотація:

Percolation networks have been widely used in the description of porous media but are now found to be relevant to understand the motion of particles in cellular membranes or the nucleus of biological cells. We here study the influence of the cluster size distribution on diffusion measurements in percolation networks.

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21

Huang, Chunmao, Xingang Liang, and Quansheng Liu. "Branching random walks with random environments in time." Frontiers of Mathematics in China 9, no. 4 (July 7, 2014): 835–42. http://dx.doi.org/10.1007/s11464-014-0407-1.

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22

Rozikov, U. A. "Random walks in random environments on metric groups." Mathematical Notes 67, no. 1 (January 2000): 103–7. http://dx.doi.org/10.1007/bf02675797.

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23

SIMENHAUS, F. "Asymptotic direction for random walks in random environments." Annales de l'Institut Henri Poincare (B) Probability and Statistics 43, no. 6 (November 2007): 751–61. http://dx.doi.org/10.1016/j.anihpb.2006.10.003.

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24

Golosov, A. O. "Limit Theorems for Random Walks in Symmetric Random Environments." Theory of Probability & Its Applications 29, no. 2 (January 1985): 266–80. http://dx.doi.org/10.1137/1129037.

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25

Butov, A. A. "Random walks in random environments of a general type." Stochastics and Stochastic Reports 48, no. 3-4 (June 1994): 145–60. http://dx.doi.org/10.1080/17442509408833904.

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26

Le Doussal, Pierre. "First-passage time for random walks in random environments." Physical Review Letters 62, no. 26 (June 26, 1989): 3097. http://dx.doi.org/10.1103/physrevlett.62.3097.

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27

Blondel, Oriane, Marcelo R. Hilário, and Augusto Teixeira. "Random walks on dynamical random environments with nonuniform mixing." Annals of Probability 48, no. 4 (July 2020): 2014–51. http://dx.doi.org/10.1214/19-aop1414.

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28

Redig, Frank, and Florian Völlering. "Random walks in dynamic random environments: A transference principle." Annals of Probability 41, no. 5 (September 2013): 3157–80. http://dx.doi.org/10.1214/12-aop819.

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29

Comets, Francis, and Ofer Zeitouni. "Gaussian fluctuations for random walks in random mixing environments." Israel Journal of Mathematics 148, no. 1 (December 2005): 87–113. http://dx.doi.org/10.1007/bf02775433.

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30

Avena, L., O. Blondel, and A. Faggionato. "Analysis of random walks in dynamic random environments viaL2-perturbations." Stochastic Processes and their Applications 128, no. 10 (October 2018): 3490–530. http://dx.doi.org/10.1016/j.spa.2017.11.010.

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31

Durrett, Richard. "Multidimensional random walks in random environments with subclassical limiting behavior." Communications in Mathematical Physics 104, no. 1 (March 1986): 87–102. http://dx.doi.org/10.1007/bf01210794.

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32

Le Doussal, P., and J. Machta. "Self-avoiding walks in quenched random environments." Journal of Statistical Physics 64, no. 3-4 (August 1991): 541–78. http://dx.doi.org/10.1007/bf01048306.

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33

Bricmont, Jean, and Antti Kupiainen. "Random Walks in Space Time Mixing Environments." Journal of Statistical Physics 134, no. 5-6 (February 21, 2009): 979–1004. http://dx.doi.org/10.1007/s10955-009-9689-1.

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34

Shussman, Yossi, and Amnon Aharony. "Self-avoiding walks on random fractal environments." Journal of Statistical Physics 80, no. 1-2 (July 1995): 147–67. http://dx.doi.org/10.1007/bf02178357.

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35

Fisher, Daniel S., Daniel Friedan, Zongan Qiu, Scott J. Shenker, and Stephen H. Shenker. "Random walks in two-dimensional random environments with constrained drift forces." Physical Review A 31, no. 6 (June 1, 1985): 3841–45. http://dx.doi.org/10.1103/physreva.31.3841.

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36

Menshikov, M. V., and Andrew R. Wade. "Logarithmic speeds for one-dimensional perturbed random walks in random environments." Stochastic Processes and their Applications 118, no. 3 (March 2008): 389–416. http://dx.doi.org/10.1016/j.spa.2007.04.011.

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37

Bolthausen, Erwin, and Ofer Zeitouni. "Multiscale analysis of exit distributions for random walks in random environments." Probability Theory and Related Fields 138, no. 3-4 (December 1, 2006): 581–645. http://dx.doi.org/10.1007/s00440-006-0032-3.

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38

Biskup, Marek, and Pierre-François Rodriguez. "Limit theory for random walks in degenerate time-dependent random environments." Journal of Functional Analysis 274, no. 4 (February 2018): 985–1046. http://dx.doi.org/10.1016/j.jfa.2017.12.002.

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39

Gao, Fuqing. "Laws of iterated logarithm for transient random walks in random environments." Frontiers of Mathematics in China 10, no. 4 (June 25, 2015): 857–74. http://dx.doi.org/10.1007/s11464-015-0481-z.

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40

Rémillard, Bruno, and Jean Vaillancourt. "Combining Losing Games into a Winning Game." Fluctuation and Noise Letters 18, no. 01 (January 9, 2019): 1950003. http://dx.doi.org/10.1142/s0219477519500032.

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Анотація:

Parrondo’s paradox is extended to regime switching random walks in random environments. The paradoxical behavior of the resulting random walk is explained by the effect of the random environment. Full characterization of the asymptotic behavior is achieved in terms of the dimensions of some random subspaces occurring in Oseledec’s theorem. The regime switching mechanism gives our models a richer and more complex asymptotic behavior than the simple random walks in random environments appearing in the literature, in terms of transience and recurrence.

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41

Zeitouni, Ofer, and Francis Comets. "A law of large numbers for random walks in random mixing environments." Annals of Probability 32, no. 1B (January 2004): 880–914. http://dx.doi.org/10.1214/aop/1079021467.

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42

Bolthausen, Erwin, and Ilya Goldsheid. "Recurrence and Transience of Random Walks¶in Random Environments on a Strip." Communications in Mathematical Physics 214, no. 2 (November 2000): 429–47. http://dx.doi.org/10.1007/s002200000279.

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43

Bramson, Maury, Ofer Zeitouni, and Martin P. W. Zerner. "Shortest spanning trees and a counterexample for random walks in random environments." Annals of Probability 34, no. 3 (May 2006): 821–56. http://dx.doi.org/10.1214/009117905000000783.

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44

Zhang, Xiaomin, and Dihe Hu. "THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS." Acta Mathematica Scientia 26, no. 4 (October 2006): 615–28. http://dx.doi.org/10.1016/s0252-9602(06)60088-x.

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45

Lenci, Marco. "Central limit theorem and recurrence for random walks in bistochastic random environments." Journal of Mathematical Physics 49, no. 12 (December 2008): 125213. http://dx.doi.org/10.1063/1.3005226.

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46

Kawazu, Kiyoshi, Yozo Tamura, and Hiroshi Tanaka. "Limit theorems for one-dimensional diffusions and random walks in random environments." Probability Theory and Related Fields 80, no. 4 (1989): 501–41. http://dx.doi.org/10.1007/bf00318905.

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47

Schulz, Beatrix, and Steffen Trimper. "Random walks in two-dimensional glass-like environments." Physics Letters A 256, no. 4 (June 1999): 266–71. http://dx.doi.org/10.1016/s0375-9601(99)00245-5.

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48

Joye, Alain, and Marco Merkli. "Dynamical Localization of Quantum Walks in Random Environments." Journal of Statistical Physics 140, no. 6 (August 14, 2010): 1025–53. http://dx.doi.org/10.1007/s10955-010-0047-0.

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49

Machta, J., and T. R. Kirkpatrick. "Self-avoiding walks and manifolds in random environments." Physical Review A 41, no. 10 (May 1, 1990): 5345–56. http://dx.doi.org/10.1103/physreva.41.5345.

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50

LENCI, MARCO. "RECURRENCE FOR PERSISTENT RANDOM WALKS IN TWO DIMENSIONS." Stochastics and Dynamics 07, no. 01 (March 2007): 53–74. http://dx.doi.org/10.1142/s0219493707001937.

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Анотація:

We discuss the question of recurrence for persistent, or Newtonian, random walks in ℤ2, i.e. random walks whose transition probabilities depend both on the walker's position and incoming direction. We use results by Tóth and Schmidt–Conze to prove recurrence for a large class of such processes, including all "invertible" walks in elliptic random environments. Furthermore, rewriting our Newtonian walks as ordinary random walks in a suitable graph, we gain a better idea of the geometric features of the problem, and obtain further examples of recurrence.

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