On returns to the starting site in lattice random walks

Barry D. Hughes

Physica A: Statistical Mechanics and its Applications, 1986, vol. 134, issue 2, 443-457

Abstract: In sufficiently low-dimensional systems, the conditional mean time to return to the starting site (conditional upon return eventually occuring) is infinite. We examine the conditional mean time τn to return in a walk of finite duration n steps. For walks of Pólya type, τn is found asymptotically proportional to `√n, nlog2 n, √n and log n in dimensions 1, 2, 3 and 4 respectively. Results are also given for walks with long-ranged transitions, and for a one-dimensional walk in a central potential.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:134:y:1986:i:2:p:443-457

DOI: 10.1016/0378-4371(86)90058-0

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