Preprints, Working Papers, ... Year : 2018

The maximal flow from a compact convex subset to infinity in first passage percolation on Z^d

Abstract

We consider the standard first passage percolation model on Z^d with a distribution G on R+ that admits an exponential moment. We study the maximal flow between a compact convex subset A of R^d and infinity. The study of maximal flow is associated with the study of sets of edges of minimal capacity that cut A from infinity. We prove that the rescaled maximal flow between nA and infinity φ(nA)/n^ (d−1) almost surely converges towards a deterministic constant depending on A. This constant corresponds to the capacity of the boundary ∂A of A and is the integral of a deterministic function over ∂A. This result was shown in dimension 2 and conjectured for higher dimensions by Garet in [6].
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Dates and versions

hal-01831419 , version 1 (05-07-2018)
hal-01831419 , version 2 (22-11-2018)

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Barbara Dembin. The maximal flow from a compact convex subset to infinity in first passage percolation on Z^d. 2018. ⟨hal-01831419v2⟩
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