How a random walk covers a finite lattice

M.J.A.M. Brummelhuis and H.J. Hilhorst

Physica A: Statistical Mechanics and its Applications, 1992, vol. 185, issue 1, 35-44

Abstract: A random walker is confined to a finite periodic d-dimensional lattice of N initially white sites. When visited by the walk a site is colored black. After t steps of the walk, for t scaled appropriately with N, we determined the structure of the set of white sites. The variance of their number has a line of critical points in the td plane, which separates a mean-field region from a region with enhanced fluctuations. At d = 2 the critical point becomes a critical interval. Moreover, for d = 2 the set of white sites is fractal with a fractal dimensionality whose t-dependence we determine.

Date: 1992
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:185:y:1992:i:1:p:35-44

DOI: 10.1016/0378-4371(92)90435-S

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