Skip to main content

All Questions

Filter by
Sorted by
Tagged with
3 votes
2 answers
224 views

Measures with superexponential moments on finitely generated groups

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 ...
Takao Hishikori's user avatar
7 votes
1 answer
274 views

Uniqueness of stationary measures for $(G,\mu)$ boundaries

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 $\...
Ilya Gekhtman's user avatar
4 votes
1 answer
288 views

Radon-Nikodym derivative of the group action on the Furstenberg-Poisson boundary of lamplighter groups

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 $G_d$ (...
Bharath's user avatar
  • 93
1 vote
1 answer
208 views

Absolute continuity of harmonic measure for a random walk and its reflection

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 $\partial G$....
Yellow Pig's user avatar
  • 2,964
3 votes
3 answers
394 views

When is the minimal Martin boundary closed?

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}\...
Yellow Pig's user avatar
  • 2,964
3 votes
0 answers
157 views

Question about martin boundaries of random walks induced on transient subgroups

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 $\...
Yellow Pig's user avatar
  • 2,964