Simple symmetrical exclusion process and the heat equation Proceso de exclusión simple simétrico y la ecuación de calor

Abstract

Our main focus is to motivate the reader for the study of particle systems and for the reader to understand, in a more or less heuristic and intuitive way, the deduction of partial differential equations through underlying microscopic systems with probabilistic dynamics. For this, we are going to use the model called symmetric simple exclusion process in contact with reservoirs. The partial differential equation involved is the heat equation with Dirichlet conditions.