Monotone interaction of walk and graph: recurrence versus transience

TL;DR

This paper investigates how monotone interactions influence the recurrence or transience of random walks on integer lattice domains, focusing on how domain growth caused by visits affects walk behavior.

Contribution

It introduces a model where monotone interactions induce domain growth based on walk visits, analyzing the impact on recurrence and transience.

Findings

Monotone interactions can alter the recurrence-transience phase transition.

Domain growth driven by walk visits affects long-term walk behavior.

The model provides insights into dynamic boundary effects on random walks.

Abstract

We consider recurrence versus transience for models of random walks on domains of $\mathbb{Z}^d$, in which monotone interaction enforces domain growth as a result of visits by the walk (or probes it sent), to the neighborhood of domain boundary.