A Lower Estimate for Central Probabilities on Polycyclic Groups

Alexopoulos, G.

Canadian journal of mathematics, Tome 44 (1992) no. 5, pp. 897-910

Résumé

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.

Détail

DOI : 10.4153/CJM-1992-055-8

Mots-clés : 31C05, 43A05, 60B15, Polycyclic groups, volume growth, convolution power, heat kernel

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