Large Favourite Sites of Simple Random Walk and the Wiener Process
Endre Csáki, Hungarian Academy of Sciences
Zhan Shi, Université de Paris VI
Abstract
Let $U(n)$ denote the most visited point by a
simple symmetric random walk ${ S_k}_{kge 0}$ in
the first $n$ steps. It is known that $U(n)$ and
$max_{0le kle n} S_k$ satisfy the same law of the iterated
logarithm, but have different upper functions (in the sense of
P. Lévy). The distance between them however turns out to be transient.
In this paper, we establish the exact rate of escape of this distance.
The corresponding problem for the Wiener process is also studied.
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