04/12/2008, 15:00 — 16:00 — Room P8, Mathematics Building, IST Patrícia Gonçalves, Universidade do Minho, Portugal
Partial Differential Equations ans Stochastic Differential Equations Arising in Particle Systems
In this talk, I will introduce a classical example of Particle System: the Simple Exclusion Process. I will give the notion of hydrodynamic limit, which is a Law of Large Numbers for the empirical measure and I will explain how to derive from the microscopic dynamics between particles a partial differential equation describing the evolution of the density profile. For the Simple Exclusion Process, in the Symmetric case we will get to the heat equation while in the Asymmetric case to the Burgers equation. Finally, I will introduce the Central Limit theorem for the empirical measure and the limiting process turns out to be a solution of a stochastic differential equation.