On the non-equivalence of two standard random walks

O. Bénichou, K. Lindenberg and G. Oshanin

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 18, 3909-3911

Abstract: We focus on two models of nearest-neighbour random walks on d-dimensional regular hyper-cubic lattices that are usually assumed to be identical—the discrete-time Polya walk, in which the walker steps at each integer moment of time, and the Montroll–Weiss continuous-time random walk in which the time intervals between successive steps are independent, exponentially and identically distributed random variables with mean 1. We show that while for symmetric random walks both models indeed lead to identical behaviour in the long time limit, when there is an external bias they lead to markedly different behaviour.

Keywords: Polya random walk; Montroll–Weiss random walk; External bias (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:18:p:3909-3911

DOI: 10.1016/j.physa.2013.04.049

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