Large Deviations at Level 2.5 for Random Walks in Random Media

For Markov processes converging towards non-equilibrium steady-states, the large deviations at Level 2.5 characterize the joint distribution of the time-averaged density and of the time-averaged flows that can be seen in a long dynamical trajectory. After a brief introduction, this general framework will be illustrated with three examples of one-dimensional disordered models:

(i) the Sinai Random Walk on a ring, where each site has its own probabilities to induce the next jump to the right or to the left 

(ii) the Directed Trap model on a ring, where each site has its own trapping time

(iii) the Sisyphus process in a random landscape, where each position has its own reset rate towards the origin