Hydrodynamics, fluctuations, and universality of exclusion processes
By: Patricia Goncalves
From: Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
At: Building C2, room 2.4.16
[2026-04-16]
In the seventies, Frank Spitzer introduced interacting particle systems (IPS) to the mathematics community. These systems consist of particles evolving randomly according to Markovian dynamics that conserve certain quantities. IPS were already known in the physics and biophysics communities and serve as toy models for a variety of interesting phenomena. One of the most classical IPS is the exclusion process, where particles evolve in a discrete space according to a transition probability, but at each site, only one particle is allowed.
One of the goals of studying these models is to derive their hydrodynamic limit, i.e., to deduce the macroscopic equations governing the space-time evolution of the conserved quantities of the system from the underlying random motion of the microscopic particles.
In this talk, I will review the derivation of these limits for the exclusion process. I will also discuss their equilibrium fluctuations, i.e., the fluctuations around the typical profile when the system starts from the invariant measure.
Our focus will then shift to the two-species exclusion process, a system with two conservation laws, namely particles of type A and B. We will see that for proper linear combinations of the conserved quantities, their evolution is autonomous. This advances our understanding of the universal behavior of these systems.
This presentation is based on joint work with G. Cannizzaro, R. Misturini, and A. Occelli.