Seminario EDP UAM-ICMAT
Renormalisation of singular SPDEs in correlated environment
Ponente: Nicolas Clozeau (University of Toulon)Fecha: viernes 12 de junio de 2026 - 12:30Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
I will present joint work with Harprit Singh (Swiss NSF Fellow at SISSA) on the renormalisation of parabolic singular stochastic PDEs (SPDEs) in correlated media. I will focus on the example of the Parabolic Anderson Model in a correlated random environment, which describes the expected density of diffusing particles in the presence of random sources and sinks and can be interpreted as a model for populations or branching processes evolving in a disordered medium. The main challenge is that the equation is ill-posed and requires a renormalisation procedure to construct a pathwise solution theory.
First, I will describe the renormalisation procedure based on the theory of regularity structures, which allows us to identify the relevant counterterms and establish a pathwise solution theory. Second, I will present an inductive approach for deriving stochastic estimates on the underlying model, providing the key probabilistic bounds required for the renormalisation analysis.
