In this talk I will introduce an example of Particle System - the Simple Exclusion Process:
the symmetric and asymmetric case. 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. I will also introduce the Central
Limit Theorem for the empirical measure and the limiting process turns
out to be a solution of a stochastic differential equation. Finally I
will superpose both dynamics in different time scales to study the effect on the limit equilibrium density fluctuation field. |