A weak universality result for the parabolic Anderson model

Tuesday, September 26, 2017
Ora Inizio: 
Ora Fine: 
Nicolas Perkowski
Humboldt-Universität zu Berlin

Abstract: We consider a class of nonlinear population models on a two-dimensional lattice which are influenced by a small random potential, and we show that on large temporal and spatial scales the population density is well described by the continuous parabolic Anderson model, a linear but singular stochastic PDE. The proof is based on a discrete formulation of paracontrolled distributions on unbounded lattices which is of independent interest because it can be applied to prove the convergence of a wide range of lattice models. This is joint work with Jörg Martin.