Maximum occupation time of a transient excited random walk on Z

Abstract

We consider a transient excited random walk on $Z$ and study the asymptotic behavior of the occupation time of a currently most visited site. In particular, our results imply that, in contrast to the random walks in random environment, a transient excited random walk does not spend an asymptotically positive fraction of time at its favorite (most visited up to a date) sites.

Revised version. The proof has been updated to clarify the passage from the excited random walk to the associated branching-process representation, using a triangular-array formulation rather than only fixed-level distributional identities. Several related renewal and Borel--Cantelli arguments have also been tightened