Abstract
For a general class of lattice spin systems, we prove that an abstract Gaussian concentration bound implies positivity of the lower relative entropy density. As a consequence, we obtain uniqueness of translation-invariant Gibbs measures from the Gaussian concentration bound in this general setting. This extends earlier results with a different and very short proof.
| Original language | English |
|---|---|
| Number of pages | 14 |
| Journal | Entropy: international and interdisciplinary journal of entropy and information studies |
| Volume | 24 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 2022 |
Keywords
- lattice spin systems
- translation-invariant Gibbs measure
- concentration inequality
- relative entropy density