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

Rodrigo B. Alves; Giulio Iacobelli; Glauco Valle

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arXiv · 2211.05715

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

Rodrigo B. Alves·Giulio Iacobelli·Glauco Valle

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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.

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Rodrigo B. Alves, Giulio Iacobelli, Glauco Valle. 2022-11-10. A note on transience of generalized many-dimensional excited random walks. https://arxiv.org/abs/2211.05715

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