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The Allen-Cahn equation with weakly critical initial datum

  • Tommaso Rosati (University of Warwick)
E1 05 (Leibniz-Saal)

Abstract

We study the Allen-Cahn equation in dimension 2 with white noise initial datum. In a weak coupling regime, where the nonlinearity is damped in relation to the smoothing of the initial condition, we prove Gaussian fluctuations. The effective variance that appears can be described as the solution to an ODE. Our proof builds on a Wild expansion of the solution. I will discuss ongoing applications in the perturbative study of other critical SPDEs. Joint works with Simon Gabriel, Martin Hairer, Khoa Lê and Nikos Zygouras.

Upcoming Events of this Seminar

  • Dienstag, 11.03.25 tba with Jianfeng Lu
  • Dienstag, 11.03.25 tba with Steffen Börm
  • Dienstag, 06.05.25 tba with Ilya Chevyrev
  • Dienstag, 03.06.25 tba with Mate Gerencser