Large deviation principle for the streams and the maximal flow in first passage percolation.
par
Barbara Dembin
→
Europe/Paris
Fokko du Cloux (ICJ, Bâtiment Braconnier)
Fokko du Cloux
ICJ, Bâtiment Braconnier
Description
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 \Omega in R^d and two disjoint subsets of the boundary of \Omega representing respectively the source and the sink, i.e., where the water can enter in \Omega and escape from \Omega. We are interested in the maximal flow, i.e., the maximal amount of water that can enters through \Omega per unit of time. A stream is a function on the edges that describes how the water circulates in \Omega. 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 \Omega.
