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We construct random walks taking place on the k-cells of free G-CW complexesof finite type. These random walks define operators acting on the cellulark-chains that relate nicely to the (upper) cellular k-Laplacian. As anapplication, we use this relation to show that the Novikov-Shubin invariants ofa free G-CW complex X of finite type can be recovered from quantities relatedto return probabilities of the random walks on the cells of X.

Laplacians and Random Walks on CW Complexes