Mathematics Winter School 

23/02/2021, 17:00 — 17:15 — Online
Gabriel Nahum, Mathematics PhD Student at Instituto Superior Técnico

The SSEP with open boundaries - Hydrodynamic Limit and Matrix Product Ansatz

On this talk we present the Symmetric Simple Exclusion Process (SSEP) on a finite lattice with open boundaries in 1 dimension. A description of this model is the following: we occupy arbitrarily a number of points with one particle; then, let the system evolve according to a (Simple) law of motion - a particle jumps with the same rate to its left/right site (Symmetric), iff this site is empty (Exclusion rule). The open boundaries allow us to inject/remove particles. Formally, this Interacting Particle System (IPS) is a Markov process, and on the past few decades has been actively studied in the context of Statistical Physics, providing more eyes on the inside of the world of non-equilibrium Thermodynamics.
An interesting question on the study of these IPS's is the amount of information that we can extract when going from this discrete space to a continuous one (also seen as micro-to-macro), and the description of microscopic quantities by means of macroscopic ones. On this vein, we will shortly expose the macroscopic description for the local density of particles (a Law of Large Numbers), and present a method for obtaining the exact distribution of the process on its stationary state.

See also

eim-23-02-2021-gabriel_nahum.pdf