# Student Probability Seminar

#### Random interlacements, the Gaussian free field and percolation

**Speaker:**
Maximilian Nitzschner, CIMS

**Location:**
Online

**Date:**
Wednesday, April 28, 2021, 9 a.m.

**Synopsis:**

This talk will give an introduction to the model of random interlacements, which was introduced by Sznitman and describes the local picture of a random walk on a large torus.

The vacant set of random interlacements constitutes a natural percolation model with long-range dependence, which has been extensively studied in the previous decade. We review some of the results for this model as well as the connection between random interlacements and another percolation model with long-range dependence, the level-set of the discrete Gaussian free field. Moreover, we present some recent results concerning disconnection in the strongly percolative regimes of both models, obtained in collaboration with Alberto Chiarini and Alain-Sol Sznitman.