Ergodic and Mixing Probability Measures on [SIN] Groups

W. Jaworski ()
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W. Jaworski: Carleton University

Journal of Theoretical Probability, 2004, vol. 17, issue 3, 741-759

Abstract: Abstract We prove that the concepts of completely mixing, mixing, and weakly mixing probability measures on a locally compact group in the class [SIN] are mutually equivalent. A probability measure on such a group is completely mixing if and only if it is ergodic and aperiodic. For measures that are not necessarily aperiodic ergodicity is shown to be equivalent to a mixing-like property which we call almost mixing. Some results on when a probability measure on a [SIN] group is ergodic are also developed. Our methods are based on the theory of boundaries of random walks.

Keywords: Probability measures; random walks; locally compact groups; ergodicity; mixing (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOTP.0000040297.84097.57

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