Maximum occupation time of a transient excited random walk on Z
Probability
2026-05-27 v2
Abstract
We consider a transient excited random walk on 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.
Keywords
Cite
@article{arxiv.1111.1254,
title = {Maximum occupation time of a transient excited random walk on Z},
author = {Reza Rastegar and Alexander Roitershtein},
journal= {arXiv preprint arXiv:1111.1254},
year = {2026}
}
Comments
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