Lower large deviations and laws of large numbers for maximal flows through a box in first passage percolation

DOI10.1214/09-AIHP346zbMath1221.60144arXiv0801.0967MaRDI QIDQ629790

Marie Théret, Raphaël Rossignol

Publication date: 10 March 2011

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.0967

zbMATH Keywords

law of large numberslarge deviation principleconcentration inequalityfirst passage percolationmaximal flow

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Large deviations (60F10)

Related Items (15)

Isoperimetry in supercritical bond percolation in dimensions three and higher ⋮ Limit theorems for maximum flows on a lattice ⋮ The maximal flow from a compact convex subset to infinity in first passage percolation on \(\mathbb{Z}^d \) ⋮ Size of a minimal cutset in supercritical first passage percolation ⋮ Anchored isoperimetric profile of the infinite cluster in supercritical bond percolation is Lipschitz continuous ⋮ Large deviations for the contact process in random environment ⋮ Limit of the Wulff crystal when approaching criticality for isoperimetry in 2D percolation ⋮ Maximal stream and minimal cutset for first passage percolation through a domain of \(\mathbb{R}^{d}\) ⋮ Upper large deviations for the maximal flow through a domain of \(\mathbb R^{d}\) in first passage percolation ⋮ Existence and continuity of the flow constant in first passage percolation ⋮ Existence of the anchored isoperimetric profile in supercritical bond percolation in dimension two and higher ⋮ Lower large deviations for the maximal flow through a domain of \({\mathbb{R}^d}\) in first passage percolation ⋮ Law of large numbers for the maximal flow through a domain of $\mathbb{R}^{d}$ in first passage percolation ⋮ Harry Kesten's work in probability theory ⋮ Fluctuation estimates for the multi-cell formula in stochastic homogenization of partitions

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