Philippe Thieullen

A LARGE DEVIATION PRINCIPLE FOR THE EQUILIBRIUM STATES OF HÖLDER POTENTIALS: THE ZERO TEMPERATURE CASE

Consider a α-Holder function A : Σ → ℝ and assume that it admits a unique maximizing measure μmax. For each β, we denote μβ, the unique equilibrium measure associated to βA. We show that (μβ) satisfies a Large Deviation Principle, that is, for any cylinder C of Σ, \[ \lim_{\beta \to +\infty} \frac{1}{\beta} \log \mu_{\beta}(C)=-\inf_{x \in C} I(x) \] where \[ I(x)=\sum_{n\geq0}(V\circ\sigma-V-(A-m))\circ\sigma^n(x), \quad m=\int\!A\,d\mu_{\max} \] where V(x) is any strict subaction of A.

Zero-temperature phase diagram for double-well type potentials in the summable variation class

We study the zero-temperature limit of the Gibbs measures of a class of long-range potentials on a full shift of two symbols

A Thermodynamic Formalism for Continuous Time Markov Chains with Values on the Bernoulli Space: Entropy, Pressure and Large Deviations

\{0,1\}

Transport and Large Deviations for Schrodinger Operators and Mather Measures

. These potentials were introduced by Walters as a natural space for the transfer operator. In our case, they are locally constant, Lipschitz continuous or, more generally, of summable variation. We assume there exists exactly two ground states: the fixed points

On calibrated and separating sub-actions

0^\infty

Minimizing orbits in the discrete Aubry–Mather model

and

Description of Some Ground States by Puiseux Techniques

1^\infty

Eigenfunctions of the Laplacian and associated Ruelle operator

. We fully characterize, in terms of the Peierls barrier between the two ground states, the zero-temperature phase diagram of such potentials, that is, the regions of convergence or divergence of the Gibbs measures as the temperature goes to zero.

Negative Entropy, Pressure and Zero temperature: a L.D.P. for stationary Markov Chains on [0,1]

Through this paper we analyze the ergodic properties of continuous time Markov chains with values on the one-dimensional spin lattice

An Ergodic Description of Ground States

\{1,\dots,d\}^{{\mathbb{N}}}