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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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01831419
Contributor : Barbara Dembin <>
Submitted on : Thursday, July 5, 2018 - 7:39:45 PM
Last modification on : Wednesday, April 8, 2020 - 1:40:03 PM
Document(s) archivé(s) le : Monday, October 1, 2018 - 6:20:04 PM

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  • HAL Id : hal-01831419, version 1
  • ARXIV : 1807.02316

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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-01831419v1⟩

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