We study limit theorems for random dynamical systems. We recast the random dynamics via the skew-product of the two-point motion (the Varadhan trick). Using this approach we prove several statistical properties for the system, including quenched central limit theorems with rates, quenched local limit theorem, large deviations, and decay of correlations. Then, in applications we show how to verify the general conditions using spectral properties of appropriate operators. A key application is the study of effectively expanding on average random diffeomorphisms (in any dimension, which are allowed to be dissipative). In particular, this is the first instance of proving local limit theorems in such a broad setting, without imposing restrictions on the dynamics. We provide several new examples.
We establish level-1 large deviation principles for continuous time suspension flows over countable Markov shifts, a class of non compact dynamical systems. Our results both quantify deviations of Birkhoff averages from their typical values and, importantly, provide a large deviation principle for orbits that at a fini...
Godofredo Iommi, Thomas Jordan, Anibal Velozo· 0 citations
We investigate the equilibrium thermodynamics of a Dyson gas in connection with a set of integrable statistical mechanical observables satisfying the Toda Lattice hierarchy. We prove that in the thermodynamic limit, the integrable observables are state functions satisfying a set algebraic equations of state in closed f...
The Ballistic Macroscopic Fluctuation Theory (BMFT) is a path-integral based approach to treat large-scale correlations in interacting integrable systems which, so far, has only been applied to quasi-equilibrium settings. In this paper we extend this approach to integrable quench problems and, to illustrate it, we comp...
We study a class of discrete-time interacting particle systems arising from mean-field coupled maps. We establish a Dobrushin-type estimate, a relative entropy estimate and Central Limit Theorem (CLT) type results for this class of systems. First we control the growth of the 1-Wasserstein distance between the empirical...
We study the particle number distribution of locally interacting bosonic quasi- free states, which arise in various areas of mathematical physics. We show that the particle number decomposes into an infinite sum of independent geometrically distributed random variables, confirming predictions from the physics literatur...
Fanch Coudreuse, Simone Rademacher, O. Tse· 0 citations
This paper introduces a robust strategy to establish large deviation principles for mean field interacting particle systems in T d with vanishing noise. Viewed as a Freidlin-Wentzell type problem, our approach relies on recent techniques for partial differential equations (in short PDE) on the space of probability meas...
Valentin Pesce· 0 citations
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