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### Barbara Dembin, ETH Zürich: Large deviation principle for the streams and the maximal flow in first passage percolation (Oberseminar Mathematische Stochastik)

##### Wednesday, 28.04.2021 17:00 per ZOOM: 61828242813

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 $\Omega$.
This is a joint work with Marie Théret.

Angelegt am Monday, 15.03.2021 10:28 von kollwit
Geändert am Wednesday, 21.04.2021 09:54 von kollwit
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