Spectral perturbation formulae for quenched random dynamics with applications to open systems and extreme value theory | Vidéo | Carmin.tv

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

By Gary Froyland

Appears in collection : Probabilistic techniques for random and time-varying dynamical systems / Méthodes probabilistes pour les systèmes dynamiques aléatoires et variant avec le temps

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.

Information about the video

Date of recording 06/10/2022
Date of publication 02/11/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19964703
Cite this video Froyland, Gary (06/10/2022). 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
URL https://dx.doi.org/10.24350/CIRM.V.19964703

Domain(s)

Dynamical Systems

Bibliography

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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