Random walks with local memory
Abstract
We prove a quenched invariance principle for a class of random walks in random environment on , where the walker alters its own environment. The environment consists of an outgoing edge from each vertex. The walker updates the edge at its current location to a new random edge (whose law depends on ) and then steps to the other endpoint of . We show that a native environment for these walks (i.e., an environment that is stationary in time from the perspective of the walker) consists of the wired uniform spanning forest oriented toward the walker, plus an independent outgoing edge from the walker.
Cite
@article{arxiv.1809.04710,
title = {Random walks with local memory},
author = {Swee Hong Chan and Lila Greco and Lionel Levine and Peter Li},
journal= {arXiv preprint arXiv:1809.04710},
year = {2021}
}
Comments
v3 merges several theorems into one theorem (e.g., Theorem 1.1 and Theorem 5.7 in the old version becomes Theorem 1.1). Typesetting is changed to save space. 23 pages, 8 figures