Laplacians and Random Walks on CW Complexes

Tim Höpfner

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arXiv · 2309.15509

Laplacians and Random Walks on CW Complexes

Tim Höpfner

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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.

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Tim Höpfner. 2023-09-27. Laplacians and Random Walks on CW Complexes. https://arxiv.org/abs/2309.15509

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