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.
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