Frequently visited sites of the inner boundary of simple random walk range

Izumi Okada

Stochastic Processes and their Applications, 2016, vol. 126, issue 5, 1412-1432

Abstract: This paper considers the question: how many times does a simple random walk revisit the most frequently visited site among the inner boundary points? It is known that in Z2, the number of visits to the most frequently visited site among all of the points of the random walk range up to time n is asymptotic to π−1(logn)2, while in Zd(d≥3), it is of order logn. We prove that the corresponding number for the inner boundary is asymptotic to βdlogn for any d≥2, where βd is a certain constant having a simple probabilistic expression.

Keywords: Inner boundary; Random walk range; Frequently visited site (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2015.11.008

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