BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Paweł Duch (U Poznan) DTSTART:20221110T160000Z DTEND:20221110T170000Z DTSTAMP:20260423T035907Z UID:AQFP/23 DESCRIPTION:Title: We ak universality and singular stochastic PDEs\nby Paweł Duch (U Poznan ) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\nTh e macroscopic or mesoscopic dynamics of many systems interacting with a ra ndom or chaotic environment can be described in terms of singular (i.e. cl assically ill-posed) stochastic partial differential equations. Typically\ , such stochastic PDEs depend only on a few parameters and govern the larg e-scale behavior of a huge number of different microscopic systems. This p roperty is called universality.\n\nIn the talk\, I will discuss the proof of the universality of the macroscopic scaling limit of solutions of a cla ss of parabolic stochastic PDEs with fractional Laplacian\, additive noise and polynomial non-linearity. I consider the so-called weakly non-linear regime and not necessarily Gaussian noises which are stationary\, centered \, sufficiently regular and satisfy some integrability and mixing conditio ns. The result applies to situations when the singular stochastic PDE obta ined in the scaling limit is close to critical and extends some of the exi sting universality results about the continuous interface growth models an d the phase coexistence models whose large scale behavior is governed by t he KPZ equation and the dynamical $\\Phi^4_3$ model\, respectively.\n\nThe proof uses a novel approach to singular stochastic PDEs based on the reno rmalization group flow equation. A nice feature of the method is that it c overs the full sub-critical (i.e. super-renormalizable) regime\, does not use any diagrammatic representation and avoids all combinatorial problems. Based on arXiv:2109.11380.\n LOCATION:https://researchseminars.org/talk/AQFP/23/ END:VEVENT END:VCALENDAR