Laplacians and Random Walks on CW Complexes
Geometric Topology
2023-09-28 v1 Probability
Abstract
We construct random walks taking place on the k-cells of free G-CW complexes of finite type. These random walks define operators acting on the cellular k-chains that relate nicely to the (upper) cellular k-Laplacian. As an application, we use this relation to show that the Novikov-Shubin invariants of a free G-CW complex X of finite type can be recovered from quantities related to return probabilities of the random walks on the cells of X.
Cite
@article{arxiv.2309.15509,
title = {Laplacians and Random Walks on CW Complexes},
author = {Tim Höpfner},
journal= {arXiv preprint arXiv:2309.15509},
year = {2023}
}
Comments
20 pages