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Session 34. SPDE: stochastic analysis and dynamics
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Gallavotti-Cohen fluctuation relation in infinite dimension: some recent results and examples |
Armen Shirikyan, University of Cergy-Pontoise, France
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The talk is based on the joint works with V. Jakšić (University of McGill), V. Nersesyan (University of Versailles), and C.-A. Pillet (University of Toulon)
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The Gallavotti-Cohen fluctuation relation is a general asymptotic result about probabilities of rare events under a given deterministic or stochastic dynamics. Roughly speaking, it says that, in a stationary regime, the probability of observing a negative value for the time average of the entropy production is exponentially small compared to that for the opposite value. Due to contributions of Kurchan, Lebowitz--Spohn, Maes and many others, the Gallavotti-Cohen fluctuation relation is rather well understood for many finite-dimensional stochastic systems. In this talk, I shall describe some recent results concerning the fluctuation relation in the inifnite-dimensional case and discuss some
examples.
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References-
V. Jakšić, V. Nersesyan, C.-A. Pillet, and A. Shirikyan, Large deviations from a stationary measure for a class of dissipative PDE's with random kicks , Preprint, arXiv:1212.0527, 2012.
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V. Jakšić, V. Nersesyan, C.-A. Pillet, and A. Shirikyan, Large deviations and Gallavotti-Cohen principle for dissipative PDEs with rough noise , Preprint, arXiv:1312.2964, 2013.
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