Weak Mixing of Random Walks on Groups

Christophe Cuny ()
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Christophe Cuny: Ben-Gurion University of the Negev

Journal of Theoretical Probability, 2003, vol. 16, issue 4, 923-933

Abstract: Abstract Let G be a locally compact σ-compact group with right Haar measure m and μ a regular probability measure on G. We say that μ is weakly mixing if for all g∈L ∞(G) and all f∈L 1(G) with ∫fdm=0 we have n −1∑ n k=1|〈μ k *f,g〉|→0. We show that μ is weakly mixing if and only if μ is ergodic and strictly aperiodic. To prove this we use and prove some results about unimodular eigenvalues for general Markov operators.

Keywords: locally compact group; Haar measure; random walks; weak mixing (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/B:JOTP.0000012000.54810.d2

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