Author(s):
Gonçalves, Patrícia 
Date: 2011
Persistent ID: http://hdl.handle.net/1822/16915
Origin: RepositóriUM - Universidade do Minho
Subject(s): Particle systems; Exclusion dynamics
Document details
Simple exclusion process : from randomness to determinism
Description
In this work I introduce a classical example of an Interacting Particle System: the Simple Exclusion Process. I present the notion of hydrodynamic limit, which is a Law of Large Numbers for the empirical measure and an heuristic argument 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 ($p\neq{1/2}$) to the inviscid Burgers equation. Finally, I introduce the Central Limit Theorem for the empirical measure and the limiting process turns out to be a solution of a stochastic partial differential equation.
In this work I introduce a classical example of an Interacting Particle System: the Simple Exclusion Process. I present the notion of hydrodynamic limit, which is a Law of Large Numbers for the empirical measure and an heuristic argument 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 ($p\neq{1/2}$) to the inviscid Burgers equation. Finally, I introduce the Central Limit Theorem for the empirical measure and the limiting process turns out to be a solution of a stochastic partial differential equation.
Document Type
Conference Object
Language English
Language English
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