Random walk on discrete torus and random interlacements

In this talk, we study the fragmentation of a discrete d-dimensional torus (d>=3) by a simple random walk, a basic mathematical model for the gel degradation by an enzyme. We focus on percolative properties of the largest and the second largest connected components in the complement of the trace of the random walk, as time evolves. We describe time scales on which macroscopic structural changes occur. Our analysis is based on a connection between the microscopic structure of the random walk trace in the bulk and the so-called random interlacements. This is a joint project with A. Drewitz and B. Rath (both from ETH Zurich).