Gaussian Concentration and Uniqueness of Equilibrium States in Lattice Systems

J.R. Chazottes, J. Moles, F. Redig, E. Ugalde

Research output: Contribution to journalArticleScientificpeer-review


We consider equilibrium states (that is, shift-invariant Gibbs measures) on the configuration space SZd where d≥ 1 and S 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.

Original languageEnglish
Pages (from-to)2131-2149
Number of pages19
JournalJournal of Statistical Physics
Issue number6
Publication statusPublished - 2020


  • Blowing-up property
  • Concentration inequalities
  • Equilibrium states
  • Hamming distance
  • Large deviations
  • Relative entropy

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