### Patricia Gonçalves (Instituto Superior Técnico, Lisboa, Portugal)

## ENSPM 2022 Presentation

**Title: An overview on hydrodynamic limits from interacting particles**

**Abstract: **In this talk I will explain how to derive the hydrodynamic limit from an underlying random dynamics of interacting particles.

The random dynamics conserves a quantity, that has a non-trivial evolution in space and time, and the goal is to describe the connection between the macroscopic (continuous) equations and the microscopic (discrete) system of random particles.

Among the many interacting particle systems, the exclusion process is one of the most studied dynamics. In this process, particles evolve in discrete space, and after a random time, they exchange positions according to a transition probability p(.).

Since the number of particles is conserved, an important and relevant question is to deduce, rigorously, the space-time evolution of the density from the random motion of particles.

I will present several microscopic random dynamics that have hydrodynamic limits given by the heat equation or the fractional heat equation (and variations) and how to add different boundary conditions.