Directed polymers and the Stochastic Heat Equation with heavy-tail noise

par Quentin Berger (Laboratoire de Probabilités Statistique et Modélisation, Sorbonne Université, Paris, France.)

mardi 21 juin 2022, 14:00 → 15:00 Europe/Paris

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Abstract

 

I will introduce the directed polymer model in dimension 1+d1+d, which describes a one-dimensional polymer chain placed in some disordered medium. I will give an overview of the model and I will discuss its relation to the stochastic heat equation (SHE) with multiplicative noise. This has been widely studied in the case where the disorder admits a second moment ; it corresponds to the SHE with Gaussian white noise. I will then present the results obtained in collaboration with Carsten Chong (Columbia, USA) and Hubert Lacoin (IMPA, Brazil) on the directed polymer model and the SHE with Lévy noise.

Keywords

Disordered systems, scaling limit, heavy-tail noise, directed polymers, stochastic heat equation.