Symmetric Gibbs measures

Details Symmetric Gibbs measures Symmetric Gibbs measures

1996-04-30

arxiv.org/abs/math/9604240v1

Trans. Amer. Math. Soc. 349 (1997), 2775-2811

Mathematics

Dynamical Systems

Scientific paper

We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of finitely many coordinates). The relations we consider are defined by cocycles taking values in groups, including some nonabelian ones. This generalizes (half of) the identification of the invariant ergodic probability measures for the Pascal adic transformation as exactly the Bernoulli measures---a version of de Finetti's Theorem. Generalizing the other half, we characterize the measures on subshifts of finite type that are invariant under both the adic and the shift as the Gibbs measures whose potential functions depend on only a single coordinate. There are connections with and implications for exchangeability, ratio limit theorems for transient Markov chains, interval splitting procedures, `canonical' Gibbs states, and the triviality of remote sigma-fields finer than the usual tail field.

Affiliated with

Also associated with

No associations

Rating

Symmetric Gibbs measures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Symmetric Gibbs measures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symmetric Gibbs measures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-502257