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Mathematisches Kolloquium TU Darmstadt

Andere Veranstaltungen

From fluctuations in conservative systems, to large deviations, to PDEs with irregular coefficients

Datum: 29.11.2023

Zeit: 17:15–18:15 Uhr

Fluctuations are ubiquitous in non-equilibrium systems. While their mean behavior in hydrodynamic limits is described by partial differential equations, the fluctuations around this mean can be described in terms of large deviations estimates. The analysis of such large deviations has led to the so-called macroscopic fluctuation theory, a general framework for non-equilibrium statistical mechanics. In this talk, we will survey this link between hydrodynamic limits, large deviations, and PDEs for the example of the zero range process. We will demonstrate how the task of proving large deviations estimates leads to the analysis of PDEs with irregular coefficients in critical spaces and to Gamma convergence. Finally, by developing a nonlinear extension of the DiPerna-Lions theory of renormalized solutions, we solve a long-standing open problem in the proof of a full large deviation principle for the zero-range process.


Benjamin Gess, Universität Bielefeld & MPI Leipzig


TU Darmstadt, S2|08 171 (Uhrturm-Hörsaal)
Hochschulstraße 4, 64289 Darmstadt


Technische Universität Darmstadt

Fachbereich Mathematik - Stochastik
Schlossgartenstraße 7
64289 Darmstadt
Telefon: +49 6151 16-23380
Telefax: +49 6151 16-23381


Goethe-Universität Frankfurt am Main, Johannes Gutenberg-Universität Mainz

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