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
This is a weekly series of informal talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..