Quenched Linear Response for Smooth Expanding on Average Cocycles

We establish an abstract quenched linear response result for random dynamical systems, which we then apply to the case of smooth expanding on average cocycles on the unit circle. In sharp contrast to the existing results in the literature, we deal with the class of random dynamics that does not nece...

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 399; no. 1; pp. 423 - 452
Main Authors Dragičević, Davor, Giulietti, Paolo, Sedro, Julien
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2023
Springer Nature B.V
Subjects
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Quenching
Relativity Theory
Theoretical
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Summary:We establish an abstract quenched linear response result for random dynamical systems, which we then apply to the case of smooth expanding on average cocycles on the unit circle. In sharp contrast to the existing results in the literature, we deal with the class of random dynamics that does not necessarily exhibit uniform decay of correlations. Our techniques rely on the infinite-dimensional ergodic theory and in particular, on the study of the top Oseledets space of a parametrized transfer operator cocycle. Finally, we exhibit a surprising phenomenon: a random system and a smooth observable for which quenched linear response holds, but annealed response fails.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-022-04560-1