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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Reference55 articles.
1. An example of a Kolmogorov automorphism that is not a Bernoulli shift
2. Mester P. (2011) A factor of i.i.d. with uniform marginals and infinite clusters spanned by equal labels. arXiv:1111.3067
3. Sly A. (2009) Personal communication.
4. Factors of Bernoulli shifts are Bernoulli shifts
5. A monotone Sinai theorem
Cited by
29 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献