Evolution of concentration under lattice spin-flip dynamics - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

Evolution of concentration under lattice spin-flip dynamics

Pierre Collet
  • Fonction : Auteur
  • PersonId : 1093514
Frank Redig
  • Fonction : Auteur

Résumé

We consider spin-flip dynamics of configurations in {−1, 1} ^{Z^d} , and study the time evolution of concentration inequalities. For "weakly interacting" dynamics we show that the Gaussian concentration bound is conserved in the course of time and it is satisfied by the unique stationary Gibbs measure. Next we show that, for a general class of translation-invariant spin-flip dynamics, it is impossible to evolve in finite time from a low-temperature Gibbs state towards a measure satisfying the Gaussian concentration bound. Finally, we consider the time evolution of the weaker uniform variance bound, and show that this bound is conserved under a general class of spin-flip dynamics.
Fichier principal
Vignette du fichier
ConFlip15_03_2021-JR.pdf (373.77 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03169379 , version 1 (15-03-2021)

Identifiants

  • HAL Id : hal-03169379 , version 1

Citer

Jean-René Chazottes, Pierre Collet, Frank Redig. Evolution of concentration under lattice spin-flip dynamics. 2021. ⟨hal-03169379⟩

Collections

TDS-MACS IP_PARIS
13 Consultations
34 Téléchargements

Partager

Gmail Facebook X LinkedIn More