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Equidistribution of dense subgroups on nilpotent Lie groups

Published online by Cambridge University Press:  23 June 2009

EMMANUEL BREUILLARD
Affiliation:
Ecole Polytechnique, 91128 Palaiseau, France (email: emmanuel.breuillard@math.polytechnique.fr)
Corresponding

Abstract

Let Γ be a dense subgroup of a simply connected nilpotent Lie group G generated by a finite symmetric set S. We consider the n-ball Sn for the word metric induced by S on Γ. We show that Sn (with uniform measure) becomes equidistributed on G with respect to the Haar measure as n tends to infinity. We also prove the analogous result for random walk averages.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2009

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