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    Amenability and superharmonic functions

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    Date
    1993
    Author
    Northshield, Sam
    Publisher
    Proceedings of the American Mathematical Society
    Metadata
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    Subject
    Amenable group
    superharmonic function
    Martin boundary
    random walk
    Abstract
    Let G be a countable group and u a symmetric and aperiodic probability measure on G . We show that G is amenable if and only if every positive superharmonic function is nearly constant on certain arbitrarily large subsets of G. We use this to show that if G is amenable, then the Martin boundary of G contains a fixed point. More generally, we show that G is amenable if and only if each member of a certain family of G-spaces contains a fixed point.
    Description
    This article has been published in the October 1993 issue of Proceedings of the American Mathematical Society.
    URI
    http://hdl.handle.net/1951/69948
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    • Mathematics Faculty Work [20]

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