Mathematics – Dynamical Systems
Scientific paper
2008-06-05
Mathematics
Dynamical Systems
Scientific paper
We analyze some properties of maximizing stationary Markov probabilities on the Bernoulli space $[0,1]^\mathbb{N}$, More precisely, we consider ergodic optimization for a continuous potential $A$, where $A: [0,1]^\mathbb{N}\to \mathbb{R}$ which depends only on the two first coordinates. We are interested in finding stationary Markov probabilities $\mu_\infty$ on $ [0,1]^\mathbb{N}$ that maximize the value $ \int A d \mu,$ among all stationary Markov probabilities $\mu$ on $[0,1]^\mathbb{N}$. This problem correspond in Statistical Mechanics to the zero temperature case for the interaction described by the potential $A$. The main purpose of this paper is to show, under the hypothesis of uniqueness of the maximizing probability, a Large Deviation Principle for a family of absolutely continuous Markov probabilities $\mu_\beta$ which weakly converges to $\mu_\infty$. The probabilities $\mu_\beta$ are obtained via an information we get from a Perron operator and they satisfy a variational principle similar to the pressure. Under the hypothesis of $A$ being $C^2$ and the twist condition, that is, $\frac{\partial^2 A}{\partial_x \partial_y} (x,y) \neq 0$, for all $(x,y) \in [0,1]^2$, we show the graph property.
Lopes Artur O.
Mohr Joseph John
Souza Rafael R.
Thieullen Philippe
No associations
LandOfFree
Negative Entropy, Zero temperature and stationary Markov Chains on the interval 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 Negative Entropy, Zero temperature and stationary Markov Chains on the interval, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Negative Entropy, Zero temperature and stationary Markov Chains on the interval will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-128353