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Factors of IID on Trees

Published online by Cambridge University Press:  06 December 2016

RUSSELL LYONS
RUSSELL LYONS*
Affiliation:
Department of Mathematics, Indiana University, Rawles Hall, 831 East 3rd Street, Bloomington, IN 47405, USA (e-mail: rdlyons@indiana.edu)
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Abstract

Classical ergodic theory for integer-group actions uses entropy as a complete invariant for isomorphism of IID (independent, identically distributed) processes (a.k.a. product measures). This theory holds for amenable groups as well. Despite recent spectacular progress of Bowen, the situation for non-amenable groups, including free groups, is still largely mysterious. We present some illustrative results and open questions on free groups, which are particularly interesting in combinatorics, statistical physics and probability. Our results include bounds on minimum and maximum bisection for random cubic graphs that improve on all past bounds.

Keywords

Primary 05C3005C7005C8037A3537A5060G10Secondary 60G15

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Type
Paper
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Combinatorics, Probability and Computing , Volume 26 , Issue 2 , March 2017 , pp. 285 - 300
Copyright
Copyright © Cambridge University Press 2016 

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