Factors of IID on trees

Classical ergodic theory for integer-group actions uses entropy as a complete invariant for isomorphism of IID (independent, identically dis- tributed) 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.


Publication Date:
Sep 03 2019
Date Submitted:
Nov 30 2018
ISSN:
1469-2163
Citation:
Combinatorics, Probability and Computing
26
2

Note: The status of this file is: public



 Record created 2018-11-30, last modified 2019-04-03

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