Brownian motion and transient groups
Annales de l'Institut Fourier, Volume 33 (1983) no. 2, pp. 241-261.

In this paper I consider M ˜M a covering of a Riemannian manifold M. I prove that Green’s function exists on M ˜ if any and only if the symmetric translation invariant random walks on the covering group G are transient (under the assumption that M is compact).

Dans cet article, je considère M ˜M un revêtement riemannien. Je démontre que l’existence de la fonction de Green sur M ˜ est équivalente au fait que G, le groupe de revêtement, est “transient" (à condition que M soit compacte).

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Varopoulos, Nicolas Th. Brownian motion and transient groups. Annales de l'Institut Fourier, Volume 33 (1983) no. 2, pp. 241-261. doi : 10.5802/aif.926. http://www.numdam.org/articles/10.5802/aif.926/

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