Modul: MAT971 Stochastische Prozesse

## Large deviation principle for the streams and the maximal flow in first passage percolation

Talk by Dr. Barbara Dembin

**Date:** 22.09.21 **Time:** 17.15 - 18.15 **Room:** ETH HG G 19.1

We consider the standard first passage percolation model in the rescaled lattice Z^d/n for d>= 2: with each edge e we associate a random capacity c(e)>= 0 such that the family (c(e))_e is independent and identically distributed with a common law G. We interpret this capacity as a rate of flow, i.e., it corresponds to the maximal amount of water that can cross the edge per unit of time. We consider a bounded connected domain Ω in R^d and two disjoint subsets of the boundary of Ω representing respectively the source and the sink, i.e., where the water can enter in Ω and escape from Ω. We are interested in the maximal flow, i.e., the maximal amount of water that can enters through Ω per unit of time. A stream is a function on the edges that describes how the water circulates in Ω. In this talk, we will present a large deviation principle for streams and deduce by contraction principle an upper large deviation principle for maximal flow in Ω. This is a joint work with Marie Théret.