Modul: MAT971 Stochastische Prozesse

## Sign cluster geometry of the Gaussian free field

Prof. Dr. Pierre-Francois Rodriguez talk

**Date:** 28.11.18 **Time:** 17.15 - 18.15 **Room:** ETH HG G 43

We consider the Gaussian free field on a class of transient weighted graphs G, and show that its sign clusters fall into a regime of strong supercriticality, in which two infinite sign clusters dominate (one for each sign), and finite sign clusters are necessarily tiny, with very large probability. Examples of graphs G belonging to this class include cases in which the random walk on G exhibits anomalous diffusive behavior. Our findings also imply the existence of a nontrivial percolating regime for the vacant set of random interlacements on G. Based on joint work with A. Prévost and A. Drewitz.