Toninelli, F. L. (2023, April 25). Out of equilibrium phenomena and Stochastic PDEs [Presentation]. Oberseminar Probability and Analysis, Leipzig, Germany. http://hdl.handle.net/20.500.12708/176960
E105-07 - Forschungsbereich Mathematische Stochastik E105 - Institut für Stochastik und Wirtschaftsmathematik
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Date (published):
25-Apr-2023
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Event name:
Oberseminar Probability and Analysis
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Event date:
25-Apr-2023
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Event place:
Leipzig, Germany
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Keywords:
statistical physics; SPDEs
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Abstract:
OS Analysis-Probability I will report on mathematical progress on certain (non-linear, singular) stochastic PDEs that model the mesoscopic behaviour of some out-of-equilibrium physical systems, most notably stochastic interface growth and driven diffusive systems. Namely, the d-dimensional Stochastic Burgers equation and the KPZ equation. Scaling and Renormalization Group arguments suggest that, above the critical dimension d=2, the large-scale behaviour should be Gaussian. Our results (joint works with Cannizzaro, Erhard, Gubinelli) imply, indeed, Gaussian scaling limits in dimension d\ge 3 (for the stochastic Burgers equation) and also, at least in the regime of weak non-linearity, in the critical dimension d=2 (both for stochastic Burgers and for the Anisotropic KPZ equation)
