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Metastability of Glauber dynamics with inhomogeneous coupling disorder

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Auteurs : Pulvirenti, Elena (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : I will first introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted Hopfield model. I will then present quantitative estimates of metastability in large volumes at fixed temperatures when these systems evolve according to a Glauber dynamics, i.e. where spins flip with Metropolis rates at inverse temperature $\beta $. The main result identifies conditions ensuring that with high probability the system behaves like the corresponding system where the random couplings are replaced by their averages. More precisely, we prove that the metastability of the former system is implied with high probability by the metastability of the latter. Moreover, we consider relevant metastable hitting times of the two systems and find the asymptotic tail behaviour and the moments of their ratio. This result provides an extension of the results known for the Ising model on the the Erdos-Renyi random graph. Our proofs use the potential-theoretic approach to metastability in combination with concentration inequalities.
Based on a joint work in collaboration with Anton Bovier, Frank den Hollander, Saeda Marello and Martin Slowik.

Keywords : metastability

Codes MSC :
60K35 - Interacting random processes; statistical mechanics type models; percolation theory
60K37 - Processes in random environments
82B20 - Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B44 - Disordered systems (random Ising models, random Schrodinger operators, etc.)
82C44 - Dynamics of disordered systems (random Ising systems, etc.)

Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2742/Slides/Pulvirenti_Slides.pdf

    Informations sur la Vidéo

    Réalisateur : Petit, Jean
    Langue : Anglais
    Date de publication : 14/04/2023
    Date de captation : 03/04/2023
    Sous collection : Research talks
    arXiv category : Probability
    Domaine : Mathematical Physics ; Probability & Statistics
    Format : MP4 (.mp4) - HD
    Durée : 00:33:42
    Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2023-04-03_Pulvirenti.mp4

Informations sur la Rencontre

Nom de la rencontre : Analysis and simulations of metastable systems / Analyse et simulation de systèmes métastables
Organisateurs de la rencontre : Landim, Claudio ; Lelièvre, Tony ; Bianchi, Alessandra
Dates : 03/04/2023 - 07/04/2023
Année de la rencontre : 2023
URL Congrès : https://conferences.cirm-math.fr/2742.html

Données de citation

DOI : 10.24350/CIRM.V.20028503
Citer cette vidéo: Pulvirenti, Elena (2023). Metastability of Glauber dynamics with inhomogeneous coupling disorder. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20028503
URI : http://dx.doi.org/10.24350/CIRM.V.20028503

Voir aussi

Bibliographie

  • BOVIER, Anton, HOLLANDER, Frank den, MARELLO, Saeda, et al. Metastability of Glauber dynamics with inhomogeneous coupling disorder. arXiv preprint arXiv:2209.09827, 2022. - https://doi.org/10.48550/arXiv.2209.09827



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