Current theme: Integrable systems
Mathematics
Directed polymers and the Stochastic Heat Equation with heavy-tail noise
byQuentin Berger
Abstract:I will introduce the directed polymer model in dimension \(1+d\), 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.