Exchangeable and Gibbs measures for subshifts
主 题: Exchangeable and Gibbs measures for subshifts
报告人: Prof. Jon Aaronson (Tel Aviv University, Israel)
时 间: 2005-11-04 下午 2:30 - 3:30
地 点: 理科一号楼 1114(数学所活动)
Let X be a Borel subset of S^\\\\G where S is polish and \\\\G is countable. A
measure is called exchangeable or symmetric on X if it is supported on X
and is invariant under every Borel automorphism of X which permutes
at most finitely many coordinates.
By the de Finetti, Hewitt-Savage theorem, when X=S^\\\\G, the
extremal ( i.e. ergodic) exchangeable measures are product
measures with identical marginals. Analogues of this are obtained
using the ergodic theory of equivalence relations when S is finite,
\\\\G = N or Z^d and X is a strongly aperiodic TMS (topological Markov shift).
The symmetric measures are Gibbs measures with site determined potentials.
Gibbs measures for a multidimensional TMS may not be shift invariant, with
the consequence that equilibrium measures for such TMS\\\'s (unique and
Bernoulli in the one dimensional case) exhibit a variety of spectral properties.
(Joint work with Hitoshi Nakada and Omri Sarig.)