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

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  • Okada, Izumi

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.

Suggested Citation

  • Okada, Izumi, 2016. "Frequently visited sites of the inner boundary of simple random walk range," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1412-1432.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:5:p:1412-1432
    DOI: 10.1016/j.spa.2015.11.008
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    Cited by:

    1. Okada, Izumi, 2020. "Exponents for the number of pairs of α-favorite points of a simple random walk in Z2," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 108-138.

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