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Media type:
E-Article
Title:
Factors of IID on Trees
Contributor:
LYONS, RUSSELL
imprint:
Cambridge University Press (CUP), 2017
Published in:Combinatorics, Probability and Computing
Language:
English
DOI:
10.1017/s096354831600033x
ISSN:
0963-5483;
1469-2163
Origination:
Footnote:
Description:
<jats:p>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.</jats:p>