Séminaire MODAL'X : Francesca Cottini (LPSM)

Résumé : The model of directed polymer in random environment describes a perturbation of the simple random walk given by a random environment (disorder). The partition functions of this model have been throughly investigated in recent years, also motivated by their link with the solution of the Stochastic Heat Equation. In this talk we focus on the 2d case and we show that Gaussian fluctuations hold in the so-called quasi-critical regime, which interpolates between the sub-critical regime (where a deep understanding has by now been obtained) and the critical regime (where many key questions are still open). Our results identify the most extended regime where Gaussian fluctuations can hold, before reaching the critical regime where they fail.
This is a joint work with Francesco Caravenna and Maurizia Rossi (University of Milano-Bicocca).