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Local limit theorems and equidistribution of random walks on the Heisenberg group

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Abstract.

We prove local limit theorems for products of independent random variables on the Heisenberg group which are identically distributed with respect to an arbitrary centered and compactly supported probability measure μ. We also provide uniform estimates for translates of a bounded set by comparing μn to the associated heat kernel. This, in turn, enables us to show the equidistribution of Heisenberg-unipotent random walks on finite volume homogeneous spaces G / Γ.

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Authors and Affiliations

  1. IHES, Le Bois-Marie, 35 route de Chartres, F-91440, Bures-sur-Yvette, France

    E. Breuillard

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  1. E. Breuillard
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Correspondence to E. Breuillard.

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Submitted: October 2003 Revision: November 2004 Accepted: November 2004

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Breuillard, E. Local limit theorems and equidistribution of random walks on the Heisenberg group. GAFA, Geom. funct. anal. 15, 35–82 (2005). https://doi.org/10.1007/s00039-005-0501-3

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  • DOI: https://doi.org/10.1007/s00039-005-0501-3

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