All Questions

Let $\Gamma$ be an infinite finitely generated group and let $\nu$ be a measure on $\Gamma$ which generates a transient random walk. I was reading this paper, and the authors prove many of their ...

Let $G$ be a countable group acting minimally by homeomorphisms on a compact Hausdorff space $X$ and $\mu$ be a probability measure on $G$ whose support generates $G$ as a semigroup. Let $\nu$ is a $\...

Let $G_d$ be the Lamplighter group $G_d = \mathbb{Z}^d \wr \mathbb{Z}_2 $ and $\Gamma =\{(\bar{\eta},\tilde{0}),(\bar{0},\tilde{e_1}), \cdots,(\bar{0},\tilde{e_d})\}$ be the generator set of $G_d$ (...

Let $G$ be a hyperbolic group, and $\mu$ a (nonsymmetric) probability measure on $G$ whose support generates $G$ as a semigroup. Let $\nu$ be the associated harmonic ($\mu$ stationary) on $\partial G$....

Let $\Gamma$ be a finitely generated group and $\mu$ a symmetric measure of finite support on $\Gamma$. Let $\partial_{M}\Gamma$ be the Martin boundary of $(\Gamma,\mu)$ and let $\partial^{min}_{M}\...

Suppose $\Gamma$ is a discrete, finitely generated, non-amenable group, and consider a random walk given by a measure $\mu$. Assume the measure is symmetric, finitely generated, and the support of $\...