JournalsrmiVol. 15, No. 1pp. 117–141

Local limit theorems on some non unimodular groups

  • Emile Le Page

    Université de Bretagne-Sud, Vannes, France
  • Marc Peigné

    Université de Rennes I, Rennes, France
Local limit theorems on some non unimodular groups cover
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Abstract

Let GdG_d be the semi-direct product of R+\mathbb R^{*+} and Rd\mathbb R^d, d1d≥1 and let us consider the product group Gd,N=Gd×RNG_{d,N} = G_d \times \mathbb R^N, N1N≥1. For a large class of probability measures μ\mu on Gd,NG_{d,N}, one proves that there exists ρ(μ)[0,1]\rho (\mu) \in [0,1] such that the sequence of finite measures

{n(N+3)/2ρ(μ)nμn}n1\lbrace\frac {n^{(N+3)/2}}{\rho (\mu)^n} \mu^{*n}\rbrace_{n≥1}

converges weakly to a nondegenerate measure.

Cite this article

Emile Le Page, Marc Peigné, Local limit theorems on some non unimodular groups. Rev. Mat. Iberoam. 15 (1999), no. 1, pp. 117–141

DOI 10.4171/RMI/252