Large Deviations for Stochastic Conservation Laws

We consider parabolic scalar conservation laws perturbed by a (conservative) noise. Large deviations are investigated in the singular limit of jointly vanishing viscosity and noise. The model is supposed to feature the same behavior of "asymmetric" particles systems (e.g. TASEP) under Euler scaling.

A first large deviations principle is obtained in a space of Young measures. A "second order" large deviations principle is then discussed, including connections with the Jensen and Varadhan functional. As time allows, more recent "long correlation" models will be treated.