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1 results

  • A Lower Estimate for Central Probabilities on Polycyclic Groups

  • G. Alexopoulos
  • Journal:
    Canadian Journal of Mathematics / Volume 44 / Issue 5 / 01 October 1992
    Published online by Cambridge University Press:
    20 November 2018, pp. 897-910
    Print publication:
    01 October 1992
    • Article
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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.