Final Report Summary - LIMITTRANDOMMEDIA (Limit theorems for processes in random media)
The purpose of the project was to improve the understanding of random walk in random environment. This purpose has been achieved - In the case of ballistic environments we developed a new set of tools that enable a much more precise description of the process than was before. In particular, using these methods we can prove a local limit theorem and find invariant measures. In the balanced case we developed a new maximum principle for the non-elliptic case, which enables proving a CLT as well as homogenization of the heat equation. In the reversible case we established exact moment criteria for the existence of a non-vanishing velocity. For excited random walks we significntly improved the understanding of non-iid environments by proving a zero-one law and by analysing the multi-particle case.
In addition we got some geometric results for two-dimensional spin-glasses in low temperatures.
In addition we got some geometric results for two-dimensional spin-glasses in low temperatures.