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

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 Z(2), 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 pi(-1) (log n)(2), while in Z(d)(d >= 3), it is of order log n. We prove that the corresponding number for the inner boundary is asymptotic to beta(d) log n for any d >= 2, where beta(d) is a certain constant having a simple probabilistic expression. (C) 2015 Elsevier B.V. All rights reserved.