The Choquet-Deny theorem and distal properties of totally disconnected locally compact groups of polynomial growth
| dc.creator | Jaworski, W. | |
| dc.creator | Raja, C. R. E. | |
| dc.date | 2007-02-14 | |
| dc.date.accessioned | 2026-07-07T07:46:52Z | |
| dc.date.available | 2026-07-07T07:46:52Z | |
| dc.description | We obtain sufficient and necessary conditions for the Choquet-Deny theorem to hold in the class of compactly generated totally disconnected locally compact groups of polynomial growth, and in a larger class of totally disconnected generalized $\ov{FC}$-groups. The following conditions turn out to be equivalent when $G$ is a metrizable compactly generated totally disconnected locally compact group of polynomial growth: (i) the Choquet-Deny theorem holds for $G$; (ii) the group of inner automorphisms of $G$ acts distally on $G$; (iii) every inner automorphism of $G$ is distal; (iv) the contraction subgroup of every inner automorphism of $G$ is trivial; (v) $G$ is a SIN group. We also show that for every probability measure $μ$ on a totally disconnected compactly generated locally compact second countable group of polynomial growth, the Poisson boundary is a homogeneous space of $G$, and that it is a compact homogeneous space when the support of $μ$ generates $G$. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702407 | |
| dc.identifier | http://arxiv.org/abs/math/0702407 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123974 | |
| dc.subject | Probability | |
| dc.subject | Group Theory | |
| dc.subject | 60B15;60J50;22D40 | |
| dc.title | The Choquet-Deny theorem and distal properties of totally disconnected locally compact groups of polynomial growth | |
| dc.type | text |