Chiranjib Mukherjee (University of Muenster)

We consider the smoothed multiplicative noise stochastic heat equation (SHE) in dimen-
sion d ≥ 3. If β > 0 is a parameter that denotes the disorder strength (i.e., inverse temperature), we show the existence of a critical β ∈ (0, ∞) so that, as ε → 0, the solution of the SHE exhibits “weak
disorder” when β < β and “strong disorder” when β > β. Furthermore, we investigate the behavior
of the “quenched” and “annealed” path measures arising from the solution in the weak and strong
disorder phases.
Part of this talk is based on a joint work with A. Shamov (Weizmann Institute) and O. Zeitouni
(Weizmann Institute/ Courant Institute) and Yannic Broeker (Muenster).

Sala 5, Facultad de Matemáticas, Universidad Católica, 17:00 hrs.

Department of Mathematics

Pontifical Catholic University of Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

Center for Mathematical Modeling (CMM)

Faculty of Physical and Mathematical Sciences (FCFM)

Universidad de Chile

Beauchef 851, Edificio Norte, Piso 7,

Santiago – Chile