Rate of Decay of Concentration Functions on Discrete Groups

Todd Retzlaff ()
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Todd Retzlaff: Pardee Hall, Lafayette College

Journal of Theoretical Probability, 2003, vol. 16, issue 2, 391-399

Abstract: Abstract Given an irreducible probability measure μ on a non-compact locally compact group G, it is known that the concentration functions associated with μ converge to zero. In this note the rate of this convergence is presented in the case where G is a non-locally finite discrete group. In particular it is shown that if the volume growth V(m) of G satisfies V(m) ≥ cm D then for any compact set K we have sup g∈G μ (n)(Kg) ≤ Cn −D/2.

Keywords: concentration functions; rate of decay; locally compact groups; volume growth (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1023522727662

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