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

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.

arXiv admin note: text overlap with arXiv:2201.10666 Add some comments and remarks for a better understanding, besides correcting some typos