Homogenizations and Large Deviations

The object of study is homogenization and large deviations for various stochastic models. We start by presenting large deviation bounds for certain Hamilton-Jacobi equations. The discrete analogue of the control curves from the variational formula brings us to the study of the deterministic walks in random environments. The discretization of time in variational formula of Hamilton-Jacobi equation is related to the Frenkel-Kontorova model, for which we do the homogenization