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On the asymptotic behaviour of convolution powers of probabilities on discrete groups

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Abstract

We give examples to show that a discrete group can carry two symmetric finitely supported probabilities μ, each satisfying a local limit law µ*n(e~Cσ n n −λ, but for different λ's. This disproves a conjecture ofGerl [3].

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  1. Department of Pure Mathematics, The University of Sydney, 2006, NSW, Australia

    Donald I. Cartwright

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  1. Donald I. Cartwright
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Cartwright, D.I. On the asymptotic behaviour of convolution powers of probabilities on discrete groups. Monatshefte für Mathematik 107, 287–290 (1989). https://doi.org/10.1007/BF01517356

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