  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 ${\mathbb{Z}}^2$, 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 ${\mathbb{Z}}^d$ $(d\ge3)$, 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 $d\ge2$, where $\beta_d$ is a
certain constant having a simple probabilistic expression.
