Thierry Bodineau (IHES)

Salle 523, couloir 12-13, 5è étage

A perturbative approach to the macroscopic fluctuation theory

The typical behavior of a large class of microscopic diffusive dynamics can be described by macroscopic PDEs and the fluctuations are also well encoded by the dynamical large deviations. This macroscopic description is fully determined by 2 transport coefficients, namely the diffusion coefficient and the conductivity. A great achievement of the macroscopic fluctuation theory is to represent the density large deviations of the corresponding stationary states in terms of a macroscopic variational principle (known as the quasi-potential). For general transport coefficients, this dynamical variational principle is not explicit and a closed form has been only obtained for a restricted class of models.

In a small forcing regime, we will explain how the large deviation functional of the density can be computed perturbatively by using the macroscopic fluctuation theory. This applies to general domains in any dimension and to diffusive dynamics with arbitrary transport coefficients. [Joint work with B. Derrida]