(université de
Genève)
The seminar usually takes place on mondays at 15:15 in room 17
The nearest neighbor case for d = 1 is well understood since long, with basic results by Solomon, Sinai, and many others. The non-nearest neighbor one- dimensional case is already much more difficult. This has been investigated in papers by myself and Ilya Goldsheid, and independently by Julien Brémaud.
A basic result in higher dimensions (d ≥ 3) is the one by Bricmont-Kupiainen which proves a central limit theorem in the isotropic case, in a perturbative regime, i.e. when the disorder is small. This work is extremely complicated. In the continuous setup in Rd (also for d ≥ 3), there is a similar result by Sznitman and Zeitouni.
In the talk, I will mainly focus on a multi-scaling approach for exit distributions developed with Erich Baur (Lyon), and Ofer Zeitouni (Weizmann). Originally, with Zeitouni, it was developed for the isotropic case, but recently, with Erich Baur, it has been extended to some anisotropic situations. I will also report on a work in progress on the difficult two-dimensional case.
If you have any question, you can reach me at 0041223791169