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. |