On Soft Capacities, Quasi-stationary Distributions and the Pathwise Approach to Metastability

Autor: Alexandre Gaudillière, Alessandra Bianchi, Paolo Milanesi
Přispěvatelé: Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Università degli Studi di Padova = University of Padua (Unipd), Universita degli Studi di Padova
Rok vydání: 2020
Předmět:
Zdroj: Journal of Statistical Physics
Journal of Statistical Physics, 2020
Journal of Statistical Physics, Springer Verlag, 2020
ISSN: 1572-9613
0022-4715
DOI: 10.1007/s10955-020-02618-9
Popis: 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 ($\kappa$, $\lambda$)-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.
Comment: 29 pages, 1 figure
Databáze: OpenAIRE
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