Gaussian concentration and uniqueness of equilibrium states in lattice systems
Probability
2020-12-02 v2 Mathematical Physics
math.MP
Abstract
We consider equilibrium states (that is, shift-invariant Gibbs measures) on the configuration space where and is a finite set. We prove that if an equilibrium state for a shift-invariant uniformly summable potential satisfies a Gaussian concentration bound, then it is unique. Equivalently, if there exist several equilibrium states for a potential, none of them can satisfy such a bound.
Keywords
Cite
@article{arxiv.2006.05320,
title = {Gaussian concentration and uniqueness of equilibrium states in lattice systems},
author = {J. -R. Chazottes and J. Moles and F. Redig and E. Ugalde},
journal= {arXiv preprint arXiv:2006.05320},
year = {2020}
}
Comments
24 pages. Accepted for publication in J. Stat. Phys. (2020). Some typos have been corrected. Proposition 2.2 has been strengthened: if a Gaussian concentration bound holds then the measure is mixing, not only ergodic