Rate of Decay of Concentration Functions on Discrete Groups

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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 gεGμ (n)(Kg) ≤ Cn -D/2.

Original languageEnglish (US)
Pages (from-to)391-399
Number of pages9
JournalJournal of Theoretical Probability
Issue number2
StatePublished - Apr 2003

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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