Toninelli, F. L. (2023, January 18). An SPDE version of (W)ASEP in dimension d>2 [Presentation]. Probability and statistical mechanics seminar, Rio de Janeiro, Brazil.
I will talk about a singular non-linear SPDE that was introduced by van Beijeren, Kutner and Spohn (1985) as a continuum version of d-dimensional ASEP. The equation is "supercritical" (d>3) or critical (d=2) in the SPDE language. We show that the large-scale behavior of the equation is Gaussian in dimension d greater or equal to 3 (this mirrors analogous results by Landim, Olla, Yau et al for ASEP) and also in dimension d=2 (in the so-called weak noise limit, which corresponds to a certain 2-dimensional WASEP). The scaling is non-trivial in the sense that the non-linearity has a non-vanishing effect on the limit equation. Ongoing work with G. Cannizzaro, L. Haunschmid and M. Gubinelli.
