Weak shape theorem in first passage percolation with infinite passage times

DOI10.1214/15-AIHP686zbMath1350.60100arXiv1404.4539MaRDI QIDQ330706

Raphaël Cerf, Marie Théret

Publication date: 26 October 2016

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/1404.4539

zbMATH Keywords

time constantfirst-passage percolationweak shape theorem

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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An application of singular traces to crystals and percolation ⋮ Lower bounds for fluctuations in first-passage percolation for general distributions ⋮ Size of a minimal cutset in supercritical first passage percolation ⋮ Existence and continuity of the flow constant in first passage percolation ⋮ A shape theorem for the Orthant model ⋮ Regularity of the time constant for a supercritical Bernoulli percolation ⋮ Continuity of the time constant in a continuous model of first passage percolation ⋮ The time constant for Bernoulli percolation is Lipschitz continuous strictly above \(p_c\)

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