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End date: 2022 Ă— Start date: 2020 Ă— End date: 2019 Ă— DDC: 510 Ă— Has files: Yes Ă— Type: Text Ă— Subject: Large deviations Ă— WGL Institute: WIAS Ă—

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    Large Deviations of Continuous Regular Conditional Probabilities
    (New York, NY [u.a.] : Springer Science + Business Media B.V., 2016) van Zuijlen, W.
    We study product regular conditional probabilities under measures of two coordinates with respect to the second coordinate that are weakly continuous on the support of the marginal of the second coordinate. Assuming that there exists a sequence of probability measures on the product space that satisfies a large deviation principle, we present necessary and sufficient conditions for the conditional probabilities under these measures to satisfy a large deviation principle. The arguments of these conditional probabilities are assumed to converge. A way to view regular conditional probabilities as a special case of product regular conditional probabilities is presented. This is used to derive conditions for large deviations of regular conditional probabilities. In addition, we derive a Sanov-type theorem for large deviations of the empirical distribution of the first coordinate conditioned on fixing the empirical distribution of the second coordinate.
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    Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems
    (Basel : MDPI, 2018) Renger, D. R. Michiel
    In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager–Machlup relations. Of particular interest is the case where the microscopic system consists of random particles, and the macroscopic quantity is the empirical measure or concentration. In this work we take the particle flux as the macroscopic quantity, which is related to the concentration via a continuity equation. By a similar argument the large deviations can induce a generalised gradient or GENERIC system in the space of fluxes. In a general setting we study how flux gradient or GENERIC systems are related to gradient systems of concentrations. This shows that many gradient or GENERIC systems arise from an underlying gradient or GENERIC system where fluxes rather than densities are being driven by (free) energies. The arguments are explained by the example of reacting particle systems, which is later expanded to include spatial diffusion as well.
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    The enhanced Sanov theorem and propagation of chaos
    (Amsterdam [u.a.] : Elsevier, 2017) Deuschel, Jean-Dominique; Friz, Peter K.; Maurelli, Mario; Slowik, Martin
    We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the (-layer, enhanced) empirical measure of weakly interacting diffusions is obtained. This in turn implies a propagation of chaos result in a space of rough paths and allows for a robust analysis of the particle system and its McKean–Vlasov type limit, as shown in two corollaries.