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- W3144947089 abstract "Let $Gamma$ be a countable discrete group, $H$ a lcsc totally disconnected group and $rho : Gamma rightarrow H$ a homomorphism with dense image. We develop a general and explicit technique which provides, for every compact open subgroup $L < H$ and bi-$L$-invariant probability measure $theta$ on $H$, a Furstenberg discretization $tau$ of $theta$ such that the Poisson boundary of $(H,theta)$ is a $tau$-boundary. Among other things, this technique allows us to construct examples of finitely supported random walks on certain lamplighter groups and solvable Baumslag-Solitar groups, whose Poisson boundaries are prime, but not $L^p$-irreducible for any $p geq 1$, answering a conjecture of Bader-Muchnik in the negative. Furthermore, we give an example of a countable discrete group $Gamma$ and two spread-out probability measures $tau_1$ and $tau_2$ on $Gamma$ such that the boundary entropy spectrum of $(Gamma,tau_1)$ is an interval, while the boundary entropy spectrum of $(Gamma,tau_2)$ is a Cantor set." @default.
- W3144947089 created "2021-04-13" @default.
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- W3144947089 date "2020-06-28" @default.
- W3144947089 modified "2023-09-23" @default.
- W3144947089 title "Random walks on dense subgroups of locally compact groups" @default.
- W3144947089 hasPublicationYear "2020" @default.
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