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Let $(M,g)$ a smooth closed Riemannian manifold with non trivial first homology group $H^1(M,\mathbb{R})$. Any element of $H^1(M,\mathbb{Z})$ will define a riemannian $\mathbb{Z}$-cover of $M$ ...

If $\alpha$ is a real smooth $1$-form, and if $\mathcal C$ is the space of continuous functions $c : [0,1] \to \mathbb R^n$, endowed with the Wiener measure $w$, and if $I_\alpha : \mathcal C \to \...

Let $M$ be a connected Riemannian manifold and $x_0 \in M$. For $0 < \alpha < \frac 1 2$, let $$H = \{ c : [0,1] \to M \mid c(0) = x_0 \text{ and } \exists C>0 \text { s.t. } d(c(s), c(t)) \...

For closed manifolds, we know that the Poisson boundary is trivial due to compactness and for radially symmetric manifolds for which diffusion is one dimensional, there are A Brief Introduction to ...

In am not a probabilist, but I must do some stochastic-flavoured work on a connected Riemannian manifold $M$. A nice thing about the Brownian motion on $\mathbb R^n$ is that we may talk about its ...