Probability and Statistics Seminar   RSS

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 (p=1/2) we will get to the heat equation while in the Asymmetric case (p1/2) 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.