Finite type approximations of Gibbs measures on sofic subshifts

Details Finite type approximations of Gibbs measures on sofic subshifts Finite type approximations of Gibbs measures on sofic subshifts

2004-02-09

arxiv.org/abs/math/0402144v1

Nonlinearity 18 , 445-463 (2005)

Mathematics

Dynamical Systems

18 pages, no figures

Scientific paper

10.1088/0951-7715/18/1/023

Consider a H\"older continuous potential $\phi$ defined on the full shift $A^\nn$, where $A$ is a finite alphabet. Let $X\subset A^\nn$ be a specified sofic subshift. It is well-known that there is a unique Gibbs measure $\mu_\phi$ on $X$ associated to $\phi$. Besides, there is a natural nested sequence of subshifts of finite type $(X_m)$ converging to the sofic subshift $X$. To this sequence we can associate a sequence of Gibbs measures $(\mu_{\phi}^m)$. In this paper, we prove that these measures weakly converge at exponential speed to $\mu_\phi$ (in the classical distance metrizing weak topology). We also establish a strong mixing property (ensuring weak Bernoullicity) of $\mu_\phi$. Finally, we prove that the measure-theoretic entropy of $\mu_\phi^m$ converges to the one of $\mu_\phi$ exponentially fast. We indicate how to extend our results to more general subshifts and potentials. We stress that we use basic algebraic tools (contractive properties of iterated matrices) and symbolic dynamics.

Affiliated with

Also associated with

No associations

Rating

Finite type approximations of Gibbs measures on sofic subshifts 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 Finite type approximations of Gibbs measures on sofic subshifts, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite type approximations of Gibbs measures on sofic subshifts will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-30410