Numerical Simulations of Random Walk in Random Environment |
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Authors: | Joseph G Conlon Brian von Dohlen |
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Institution: | (1) Department of Mathematics, University of Michigan, Ann Arbor, Michigan, 48109 |
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Abstract: | This paper is concerned with the numerical simulation of a random walk in a random environment in dimension d = 2. Consider a nearest neighbor random walk on the 2-dimensional integer lattice. The transition probabilities at each site are assumed to be themselves random variables, but fixed for all time. This is the random environment. Consider a parallel strip of radius R centered on an axis through the origin. Let X
R be the probability that the walk that started at the origin exits the strip through one of the boundary lines. Then X
R is a random variable, depending on the environment. In dimension d = 1, the variable X
R converges in distribution to the Bernoulli variable, X
= 0, 1 with equal probability, as R . Here the 2-dimensional problem is studied using Gauss-Seidel and multigrid algorithms. |
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Keywords: | Numerical simulations random walks |
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