Captivity of mean-field particle systems and the related exit problems

• Autorzy: Tugaut J.
• Języki publikacji: EN

Abstrakty

EN

A mean-field system is a weakly interacting system of N particles in R^d confined by an external potential. The aim of this work is to establish a simple result about the exit problem of mean-field systems from some domains when the number of particles goes to infinity. More precisely, we prove the existence of some subsets of R^dN such that the probability of leaving these sets before any T > 0 is arbitrarily small by taking N large enough. On the one hand, we show that the number of steady states in the small-noise limit is arbitrarily large with a sufficiently large number of particles. On the other hand, using the long-time convergence of the hydrodynamical limit, we identify the steady states as N goes to infinity with the invariant probabilities of the McKean-Vlasov diffusion so that some steady states in the small-noise limit are not steady states in the large N limit.

Słowa kluczowe

EN

interacting particle system; propagation of chaos; exit time; nonconvexity; free energy; invariant probabilities

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2015
• Tom: Vol. 35, Fasc. 1
• Strony: 143--159
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Tugaut J.

• Institut Camille Jordan CNRS UMR 5208, Université Jean Monnet, Télécom Saint-Étienne, 25, rue du Docteur Rémy Annino, 42000 Saint-Étienne, France

Bibliografia

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Uwagi

This article is dedicated to Marina Sertić.

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).