Brownian motion and transient groups

Varopoulos, Nicolas Th.

Annales de l'Institut Fourier, Tome 33 (1983) no. 2, pp. 241-261.

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

In this paper I consider $\tilde{M}\to M$ a covering of a Riemannian manifold $M$. I prove that Green’s function exists on $\tilde{M}$ 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).

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