BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Giuseppe Cannizzaro (Warwick) DTSTART:20210521T163000Z DTEND:20210521T173000Z DTSTAMP:20260423T004825Z UID:PatC/39 DESCRIPTION:Title: Ed wards-Wilkinson fluctuations for the Anisotropic KPZ in the weak coupling regime\nby Giuseppe Cannizzaro (Warwick) as part of Probability and th e City Seminar\n\n\nAbstract\nIn this talk\, we present recent results on an anisotropic variant of the Kardar-Parisi-Zhang equation\, the Anisotrop ic KPZ equation (AKPZ)\, in the critical spatial dimension d=2. This is a singular SPDE which is conjectured to capture the behaviour of the fluctua tions of a large family of random surface growth phenomena but whose analy sis falls outside of the scope not only of classical stochastic calculus b ut also of the theory of Regularity Structures and paracontrolled calculus . We first prove the conjecture made in [Cannizzaro\, Erhard\, Toninelli\, "The AKPZ equation at stationarity: logarithmic superdiffusivity"]\, i.e. we show that the nonlinearity causes a logarithmically superdiffusive beh aviour at large scales and more precisely that correlation length of the s olution grows like t1/2 (log t)1/4 up to lower order correction. Motivated by the previous\, we consider the AKPZ equation in the so-called weak cou pling regime\, i.e. the equation regularised at scale N and the coefficien t of the nonlinearity tuned down by a factor (log N)-1/2\, and prove that\ , for N going to infinity\, its solution converges to a linear stochastic heat equation with renormalised coefficients.\nThe talk is based on (ongoi ng) joint work with D. Erhard and F. Toninelli.\n LOCATION:https://researchseminars.org/talk/PatC/39/ END:VEVENT END:VCALENDAR