Escape of a Uniform Random Walk from an Interval

Details Escape of a Uniform Random Walk from an Interval Escape of a Uniform Random Walk from an Interval

2005-12-22

arxiv.org/abs/physics/0512221v1

Journal of Statistical Physics 123, 1129 (2006)

Physics

Data Analysis, Statistics and Probability

8 pages, 8 figures, 2 column revtex4 format

Scientific paper

10.1007/s10955-006-9139-2

We study the first-passage properties of a random walk in the unit interval in which the length of a single step is uniformly distributed over the finite range [-a,a]. For a of the order of one, the exit probabilities to each edge of the interval and the exit time from the interval exhibit anomalous properties stemming from the change in the minimum number of steps to escape the interval as a function of the starting point. As a decreases, first-passage properties approach those of continuum diffusion, but non-diffusive effects remain because of residual discreteness effects

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