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A Lower Estimate for Central Probabilities on Polycyclic Groups

Published online by Cambridge University Press:  20 November 2018

G. Alexopoulos
G. Alexopoulos*
Affiliation:
Université de Paris-Sud, Mathématiques, Bât. 425, 91405 Orsay Cedex, France
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Abstract

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We give a lower estimate for the central value μ*n(e) of the nth convolution power μ*···*μ of a symmetric probability measure μ on a polycyclic group G of exponential growth whose support is finite and generates G. We also give a similar large time diagonal estimate for the fundamendal solution of the equation (∂/∂t + L)u = 0, where L is a left invariant sub-Laplacian on a unimodular amenable Lie group G of exponential growth.

Keywords

31C0543A0560B15Polycyclic groupsvolume growthconvolution powerheat kernel
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 5 , 01 October 1992 , pp. 897 - 910
Copyright
Copyright © Canadian Mathematical Society 1992

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