Sotiris Kotitsas (Warwick): The Stochastic Heat Equation with time correlations

We consider the multiplicative Stochastic Heat Equation

in the critical dimension d = 2 with a Gaussian random potential. We

will focus in the case where the potential is not white in time and we will study the large scale fluctuations

of the solution. This case was considered before in d ≥ 3 where it was proved that the

fluctuations converge to the Edwards-Wilkinson limit with a nontrivial effective diffusivity and an effective

variance. We prove that this result can be extended to d = 2. In particular we show that after tuning the noise strength in a critical way and renormalizing the large scale fluctuations of the solution, they converge in distribution to the

Edwards-Wilkinson model with an explicit effective variance but with a trivial effective diffusivity. Our main tools is

the Feynman-Kac formula and a fine analysis of a specific Markov chain on the space of paths that was first

introduced in d ≥ 3 for the same problem.