Fluctuations in $L^2$-region for stochastic heat equation and KPZ equation in higher dimension

2021/05/21 Fri 15:00 - 16:30
Makoto Nakashima
Nagoya University

In $d=1$, Kardar-Parisi-Zhang equations was made sense via Cole-Hopf transformation of multiplicative stochastic heat equation by Bertini and Giacomin. However, for higher dimensional case, multiplicative stochastic heat equation does not have a function valued solution and Cole-Hopf transformation could not be applied. Recently, the fluctuations of the solutions with a tuned noise strength are studied. In this talk, we prove that the scaling limit is a solution of an Edwards-Wilkinson type equation with drift term depending on the initial condition. This is a joint work with Clément Cosco (Weizmann Institute of Science) and Shuta Nakajima (the University of Basel).