On soft capacities, quasi-stationary distributions and the pathwise approach to metastability - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Statistical Physics Année : 2020

On soft capacities, quasi-stationary distributions and the pathwise approach to metastability

Résumé

Motivated by the study of the metastable stochastic Ising model at subcritical temperature and in the limit of a vanishing magnetic field, we extend the notion of (κ, λ)-capacities between sets, as well as the associated notion of soft-measures, to the case of overlapping sets. We recover their essential properties, sometimes in a stronger form or in a simpler way, relying on weaker hypotheses. These properties allow to write the main quantities associated with reversible metastable dynamics, e.g. asymptotic transition and relaxation times, in terms of objects that are associated with two- sided variational principles. We also clarify the connection with the classical “pathwise approach” by referring to temporal means on the appropriate time scale.
Fichier principal
Vignette du fichier
soft.pdf (568.76 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01850845 , version 1 (27-07-2018)
hal-01850845 , version 2 (30-04-2020)

Identifiants

Citer

Alexandre Gaudilliere, A. Bianchi, P Milanesi. On soft capacities, quasi-stationary distributions and the pathwise approach to metastability. Journal of Statistical Physics, 2020. ⟨hal-01850845v2⟩
109 Consultations
93 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More