Lattice covering time in D dimensions: theory and mean field approximation

Adolfo M. Nemirovsky and Mauricio D. Coutinho-Filho

Physica A: Statistical Mechanics and its Applications, 1991, vol. 177, issue 1, 233-240

Abstract: The covering time is the mean time for a lattice random walk (RW) to visit all N (N→∞) sites at least once. In D = 1 the problem reduces to a first-visit problem, and it has been exactly solved. In contrast, for D ⩾ 2 this novel problem is not reducible to any of the well known lattice RW problems. The theory of the D-dimensional lattice covering time is presented and contrasted against those of other RW problems such as first-visit, trapping and the number of distinct sites visited by the walk. Also, a mean field approximation of the covering problem that considers RWs of infinite range is introduced.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:177:y:1991:i:1:p:233-240

DOI: 10.1016/0378-4371(91)90158-9

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