# Analysis Seminar

#### Fluctuations around the Boltzmann equation

**Speaker:**
Sergio Simonella, ENS Lyon

**Location:**
TBA

**Date:**
Thursday, October 29, 2020, 11 a.m.

**Synopsis:**

We discuss some mathematical results on the dynamical fluctuations for the hard-sphere gas at low density (Boltzmann-Grad scaling). By developing a theory of hierarchical equations, we prove convergence of generating functionals describing random deviations from the solution to the Boltzmann equation. The limit is characterized by (i) the fluctuating Boltzmann equation with Gaussian noise; (ii) a Hamilton-Jacobi equation, in agreement with predictions on the large deviation functional. This is joint work with Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond.

**Notes:**

This is an online talk via Zoom.