A note on transience of generalized many-dimensional excited random walks

TL;DR

This paper investigates a variation of generalized excited random walks in higher dimensions with a time-decaying drift, establishing conditions under which the walk remains transient in the drift direction.

Contribution

It introduces a new model with a time-dependent lower bound on the drift and proves transience results based on the decay rate.

Findings

Transience occurs if the drift decay is slower than a certain rate.

The decay rate threshold depends on the transition dynamics.

The model extends understanding of excited random walks with time-varying parameters.

Abstract

We consider a variation of the Generalized Excited Random Walk (GERW) in dimension $d\ge 2$ where the lower bound on the drift for excited jumps is time-dependent and decays to zero. We show that if the lower bound decays slower that $n^{-\beta}$ ($n$ is time), for $\beta$ depending on the transitions of the process, the GERW is transient in the direction of the drift.