Properties of centered random walks on locally compact groups and Lie groups
| dc.creator | Dungey, Nick | |
| dc.date | 2007-03-18 | |
| dc.date.accessioned | 2026-07-07T07:52:36Z | |
| dc.date.available | 2026-07-07T07:52:36Z | |
| dc.description | The basic aim of this paper is to study asymptotic properties of the convolution powers K^(n) = K * K * ... * K of a possibly non-symmetric probability density K on a locally compact, compactly generated group G. If K is centered, we show that the Markov operator T associated with K is analytic in L^p(G) for 1<p<\infty, and establish Davies-Gaffney estimates in L^2 for the iterated operators T^n. These results enable us to obtain various Gaussian bounds on K^(n). In particular, when G is a Lie group we recover and extend some estimates of Alexopoulos and of Varopoulos for convolution powers of centered densities and for the heat kernels of centered sublaplacians. Finally, in case G is amenable, we discover that the properties of analyticity or Davies-Gaffney estimates hold only if K is centered. | |
| dc.description | 52 pages. Accepted in 2006 for publication in Revista Matematica Iberoamericana | |
| dc.identifier | https://arxiv.org/abs/math/0703530 | |
| dc.identifier | http://arxiv.org/abs/math/0703530 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125937 | |
| dc.subject | Probability | |
| dc.subject | Group Theory | |
| dc.subject | 60B15 (Primary), 60G50, 22E30, 22D05, 35B40 (Secondary) | |
| dc.title | Properties of centered random walks on locally compact groups and Lie groups | |
| dc.type | text |