Existence and continuity of the flow constant in first passage percolation

DOI10.1214/18-EJP214zbMath1415.60119arXiv1707.08766MaRDI QIDQ1990234

Raphaël Rossignol, Marie Théret

Publication date: 25 October 2018

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.08766

zbMATH Keywords

continuityminimal cutsetfirst passage percolationmaximal flow

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (5)

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 ⋮ Existence of the anchored isoperimetric profile in supercritical bond percolation in dimension two and higher ⋮ Vanishing of the anchored isoperimetric profile in bond percolation at \(p_c\)

Cites Work

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• Weak shape theorem in first passage percolation with infinite passage times
• Lower large deviations and laws of large numbers for maximal flows through a box in first passage percolation
• Upper large deviations for the maximal flow through a domain of \(\mathbb R^{d}\) in first passage percolation
• 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 tilted cylinders in two-dimensional first passage percolation
• On complete convergence in the law of large numbers for subsequences
• Surfaces with minimal random weights and maximal flows: a higher dimensional version of first-passage percolation
• Uniform pointwise ergodic theorems for classes of averaging sets and multiparameter subadditive processes
• Some limit theorems for percolation processes with necessary and sufficient conditions
• Complete convergence for arrays
• Multiparameter subadditive processes
• First passage percolation for random colorings of \(\mathbb{Z}^ d\)
• Limit theorems for maximum flows on a lattice
• Critical behavior for maximal flows on the cubic lattice
• Continuity of the time and isoperimetric constants in supercritical percolation
• Maximal stream and minimal cutset for first passage percolation through a domain of \(\mathbb{R}^{d}\)
• The Wulff crystal in Ising and percolation models. École d'Été de Probabilités de Saint-Flour XXXIV -- 2004
• First-passage percolation, network flows and electrical resistances
• 50 Years of First-Passage Percolation
• The time constant of first-passage percolation on the square lattice
• Ergodic theorems for superadditive processes.
• On the continuity of the time constant of first-passage percolation
• Asymptotic shape for the chemical distance and first-passage percolation on the infinite Bernoulli cluster
• Law of large numbers for the maximal flow through a domain of $\mathbb{R}^{d}$ in first passage percolation

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