# Large Stochastic Dynamical Models

# in
Non-Equilibrium Statistical Physics

#### Acronym: LSD

Project coordinators:

Stefano Olla (CEREMADE, Paris Dauphine)

Thierry Bodineau (CMAP, Ecole Polytechnique)

Fabio Toninelli (CNRS and Université Lyon 1)

## Scientific Themes

** Macroscopic transport phenomena**

One of our goals is to understand how macroscopic evolution
equations arise from microscopic dynamics after a coarse graining and a proper rescaling of space and time. We
are interested in the properties of the stationary non-equilibrium states. We study
the corresponding transport coefficients, e.g. thermal conductivity, and the
superdiffusion arising when these coefficients diverge in low dimensional
systems. We also analyze the fluctuations and the large deviations around the limit macroscopic
behavior.

**Slow and disordered dynamics **

In some physical systems, like
glasses, the dynamics are so slow that these systems never reach
equilibrium within observable time scales. These dynamics play a key
role in non-equilibrium physics and we study three types
of models where dynamical slowdown has very different origins:
geometric constraints, condensation and disorder.

**Interface dynamics and KPZ equation **

Interface dynamics are ubiquitous in non-
equilibrium statistical mechanics, in modeling the evolution of phase boundaries,
growth models, etc. According to the scale one is interested in, they can be effectively described via deterministic PDEs of mean-curvature type or by (highly
singular) stochastic PDEs. Both regimes pose challenging mathematical questions. Growth models are intimately related to the asymmetric lattice gases out
of equilibrium.

## Team Members

## Publications

## Postdoc Openings