# The inner boundary of random walk range

Research output: Contribution to journalArticle

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 language English 939-959 21 Journal of the Mathematical Society of Japan 68 3 https://doi.org/10.2969/jmsj/06830939 Published - Jan 1 2016

### Fingerprint

Random walk
Range of data
Simple Random Walk
Square Lattice
Large Deviations
Walk
Set of points

### All Science Journal Classification (ASJC) codes

• Mathematics(all)

### Cite this

In: Journal of the Mathematical Society of Japan, Vol. 68, No. 3, 01.01.2016, p. 939-959.

Research output: Contribution to journalArticle

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