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Spectral perturbation formulae for quenched random dynamics with applications to open systems and extreme value theory

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Auteurs : Froyland, Gary (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : We consider quasi-compact linear operator cocycles driven by an invertible ergodic process and small perturbations of this cocycle. We prove an abstract pathwise first-order formula for the leading Lyapunov multipliers. This result does not rely on random driving and applies also to sequential dynamics. We then consider the situation where the linear operator cocycle is a weighted transfer operator cocycle induced by a random map cocycle. The perturbed transfer operators are defined by the introduction of small random holes, creating a random open dynamical system. We obtain a first-order perturbation formula for the Lyapunov multipliers in this setting. Our new machinery is then deployed to create a spectral approach for a quenched extreme value theory that considers random dynamics with general ergodic invertible driving, and random observations. Further, in the setting of random piecewise expanding interval maps, we establish the existence of random equilibrium states and conditionally invariant measures for random open systems via a random perturbative approach. Finally we prove quenched statistical limit theorems for random equilibrium states arising from contracting potentials. We will illustrate the theory with some explicit examples.

Keywords : random dynamical system; extreme value theory; open dynamical system, perturbation theory

Codes MSC :
37C30 - Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
37E05 - Maps of the interval (piecewise continuous, continuous, smooth)
37H99 - Random dynamical systems

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 02/11/2022
    Date de captation : 06/10/2022
    Sous collection : Research talks
    arXiv category : Dynamical Systems
    Domaine : Dynamical Systems & ODE
    Format : MP4 (.mp4) - HD
    Durée : 00:54:59
    Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2022-10-06_Froyland.mp4

Informations sur la Rencontre

Nom de la rencontre : Probabilistic techniques for random and time-varying dynamical systems / Méthodes probabilistes pour les systèmes dynamiques aléatoires et variant avec le temps
Organisateurs de la rencontre : Bahsoun, Wael ; Demers, Mark ; Nicol, Matthew ; Pène, Françoise ; Pollicott, Mark
Dates : 03/10/2022 - 07/10/2022
Année de la rencontre : 2022
URL Congrès : https://conferences.cirm-math.fr/2601.html

Données de citation

DOI : 10.24350/CIRM.V.19964703
Citer cette vidéo: Froyland, Gary (2022). Spectral perturbation formulae for quenched random dynamics with applications to open systems and extreme value theory. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19964703
URI : http://dx.doi.org/10.24350/CIRM.V.19964703

Voir aussi

Bibliographie

  • ATNIP, Jason, FROYLAND, Gary, GONZALEZ-TOKMAN, Cecilia, et al. Perturbation formulae for quenched random dynamics with applications to open systems and extreme value theory. arXiv preprint arXiv:2206.02471, 2022. - https://doi.org/10.48550/arXiv.2206.02471



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