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Local limit theorems on some non unimodular groups.

Emile Le Page, Marc Peigné (1999)

Revista Matemática Iberoamericana

Let Gd be the semi-direct product of R*+ and Rd, d ≥ 1 and let us consider the product group Gd,N = Gd x RN, N ≥ 1. For a large class of probability measures μ on Gd,N, one prove that there exists ρ(μ) ∈ ]0,1] such that the sequence of finite measures{(n(N+3)/2 / ρ(μ)n) μ*n}n ≥ 1converges weakly to a non-degenerate measure.

Long time behavior of random walks on abelian groups

Alexander Bendikov, Barbara Bobikau (2010)

Colloquium Mathematicae

Let be a locally compact non-compact metric group. Assuming that is abelian we construct symmetric aperiodic random walks on with probabilities n ( S 2 n V ) of return to any neighborhood V of the neutral element decaying at infinity almost as fast as the exponential function n ↦ exp(-n). We also show that for some discrete groups , the decay of the function n ( S 2 n V ) can be made as slow as possible by choosing appropriate aperiodic random walks Sₙ on .

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