Focused Workshop on Random walks in Random Environment

This will be a true workshop, in the sense of concentrating the efforts of the three participants on moving forward in a specific (somewhat restricted) topic of joint interest. The subject is: Applying methods and results developed in recent years to prove central limit theorems  for random walks in so-called divergence-free random environments to tackle a problem of major interest within the more general field of random walks in random environments (RWRE), namely diffusive limits in those cases when the existence of an absolutely continuous stationary/ergodic measure of the environment-as-seen-by-the-random-walker has been established. 

 

The three participants (G. Kozma, C. Sabot, B. Toth) form a strong team in this program, as all of them contributed already with substantial results to the field. Toth and Kozma (2017) proved the strongest CLT in the context of divergence-free environments with the additional assumption of strong ellipticity. This result has been recently substantially improved (Toth, 2025, work in progress) by relaxing the strong ellipticity condition. Sabot's celebrated result (2013) about the existence of absolutely continuous stationary/ergodic measures for the so-called Dirichlet-distributed environment provided the so-far most interesting example to be further exploited. 

 

The three participants know each-other's work well and are well prepared for this collaboration.