# Probability and Mathematical Physics Seminar

#### Disconnection in two percolation models with strong correlations

**Speaker:**
Maximilian Nitzschner, ETH Zurich

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, September 20, 2019, 11:10 a.m.

**Synopsis:**

We discuss disconnection problems in two percolation models exhibiting strong correlations. These models are level sets of the Gaussian free field (GFF) and the vacant set of random interlacements, both in dimensions larger or equal to three. Specifically, we study the 'disconnection' event that either the level set of the GFF below a given level, or random interlacements, disconnect the discrete blow-up of a compact set from the boundary of an enclosing box. We give asymptotic bounds on the probability of this event in both models in their respective strongly percolative regime. Furthermore, we present results concerning the behavior of local averages of either the GFF, or occupation times of random interlacements under disconnection. In essence, the effect of disconnection amounts to a shift in the respective local average, which may be seen as an instance of entropic repulsion. This talk is based on joint work with Alberto Chiarini.