149 research outputs found
Properties of centered random walks on locally compact groups and Lie groups
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.Comment: 52 pages. Accepted in 2006 for publication in Revista Matematica
Iberoamerican
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