Zusammenfassung für den Vortrag am 25.04.2023 (15:15 Uhr)
OS Analysis-ProbabilityFabio Toninelli (Technical University of Vienna)
Out-of-equilibrium phenomena, stochastic PDEs and Gaussian limits
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 (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). The weak non-linearity limit will be discussed in much more detail in Giuseppe’s talk