Linear and nonlinear fractional PDEs from interacting particle systemsOberseminar Stochastics

by Pedro Cardoso (University of Bonn)

Thursday Dec 5, 2024, 4:30 PM → 5:30 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

In this talk, we describe the strategy for the derivation of the hydrodynamic limit for a family of long-range interacting particle systems of exclusion type with symmetric rates. The corresponding hydrodynamic equation is
                               $$\partial_t \rho = [−(−\Delta)^{\gamma/2}]\rho^m$$
for some fixed $m \in \mathcal{N}$, where $\rho$ is the density of particles in the system. For $ m = 1$, this is the fractional heat equation. For $m \geq 2$, this is the fractional porous medium equation, obtained by choosing a rate that depends on the number of particles next to the initial and final position of a jump.