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

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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 log n. 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.

Original languageEnglish
Pages (from-to)1412-1432
Number of pages21
JournalStochastic Processes and their Applications
Volume126
Issue number5
DOIs
Publication statusPublished - May 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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