The inner boundary of random walk range

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3 Citations (Scopus)

Abstract

In this paper, we deal with the inner boundary of random walk range, that is, the set of those points in a random walk range which have at least one neighbor site outside the range. If Ln be the number of the inner boundary points of random walk range in the n steps, we prove lim n→∞(L n/n) exists with probability one. Also, we obtain some large deviation result for transient walk. We find that the expectation of the number of the inner boundary points of simple random walk on the two dimensional square lattice is of the same order as n/(log n)2.

Original languageEnglish
Pages (from-to)939-959
Number of pages21
JournalJournal of the Mathematical Society of Japan
Volume68
Issue number3
DOIs
Publication statusPublished - Jan 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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