Random walk in changing environment

[摘要] We introduce the notion of Random Walk in Changing Environment (RWCE) - a random walk on a weighted graph in which the weights may change between steps. RWCE's generalize many known RW (e.g. reinforced RW, true SAW). We explore possible properties of RWCE's, and provide criteria for recurrence and transience when the underlying graph is N or a tree. We construct a RWCE on Z(2) where conductances can only change from 1 to 2 (once) but nevertheless the walk is transient, and conjecture that such behavior cannot happen when the changes do not depend on the location of the RWCE. (C) 2020 Elsevier B.V. All rights reserved.

[发布日期] 2020-12-01