The time constant of first-passage percolation on the square lattice

DOI10.2307/1426745zbMath0442.60096OpenAlexW2321266335MaRDI QIDQ3884941

J. Theodore Cox

Publication date: 1980

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1426745

zbMATH Keywords

time constantfirst-passage percolationsubadditive processes

Mathematics Subject Classification ID

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

Related Items (13)

Limiting results for the free energy of directed polymers in random environment with unbounded jumps ⋮ Comparison of limit shapes for Bernoulli first-passage percolation ⋮ Empirical Measures, Geodesic Lengths, and a Variational Formula in First-Passage Percolation ⋮ Continuity for the asymptotic shape in the frog model with random initial configurations ⋮ Continuity for the rate function of the simple random walk on supercritical percolation clusters ⋮ Tertiles and the time constant ⋮ Existence and continuity of the flow constant in first passage percolation ⋮ Asymptotic shape for the chemical distance and first-passage percolation on the infinite Bernoulli cluster ⋮ 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 \(p_c\) ⋮ Convergence towards an asymptotic shape in first-passage percolation on cone-like subgraphs of the integer lattice ⋮ First-order behavior of the time constant in Bernoulli first-passage percolation

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