Revista Matemática Iberoamericana

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Volume 15, Issue 1, 1999, pp. 117–141
DOI: 10.4171/RMI/252

Published online: 1999-04-30

Local limit theorems on some non unimodular groups

Emile Le Page[1] and Marc Peigné[2]

(1) Université de Bretagne-Sud, Vannes, France
(2) Université de Rennes I, Rennes, France

Let $G_d$ be the semi-direct product of $\mathbb R^{*+}$ and $\mathbb R^d$, $d≥1$ and let us consider the product group $G_{d,N} = G_d \times \mathbb R^N$, $N≥1$. For a large class of probability measures $\mu$ on $G_{d,N}$, one proves that there exists $\rho (\mu) \in [0,1]$ such that the sequence of finite measures $$\lbrace\frac {n^{(N+3)/2}}{\rho (\mu)^n} \mu^{*n}\rbrace_{n≥1}$$ converges weakly to a nondegenerate measure.

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Le Page Emile, Peigné Marc: Local limit theorems on some non unimodular groups. Rev. Mat. Iberoam. 15 (1999), 117-141. doi: 10.4171/RMI/252