Abstract
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 language | English |
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Pages (from-to) | 2131-2149 |
Number of pages | 19 |
Journal | Journal of Statistical Physics |
Volume | 181 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2020 |
Bibliographical note
Accepted author manuscriptKeywords
- Blowing-up property
- Concentration inequalities
- Equilibrium states
- Hamming distance
- Large deviations
- Relative entropy