Superlinearity of Geodesic Length in 2D Critical First-Passage Percolation

DOI10.1007/978-981-15-0298-9_4zbMath1446.82034arXiv1610.02593OpenAlexW2529901740MaRDI QIDQ3296396

Pengfei Tang, Michael Damron

Publication date: 7 July 2020

Published in: Sojourns in Probability Theory and Statistical Physics - II (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.02593

zbMATH Keywords

percolationgeodesicfractal dimensioncritical FPP

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) 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) Critical phenomena in equilibrium statistical mechanics (82B27) Length, area, volume, other geometric measure theory (28A75)

Related Items (7)

Size of a minimal cutset in supercritical first passage percolation ⋮ Geodesic length and shifted weights in first-passage percolation ⋮ Comparison of limit shapes for Bernoulli first-passage percolation ⋮ Empirical Measures, Geodesic Lengths, and a Variational Formula in First-Passage Percolation ⋮ Transitions for exceptional times in dynamical first-passage percolation ⋮ Exponential decay of correlations in the two-dimensional random field Ising model ⋮ The time constant for Bernoulli percolation is Lipschitz continuous strictly above \(p_c\)

Cites Work

• Unnamed Item
• Large deviation bounds for the volume of the largest cluster in 2D critical percolation
• Relations between invasion percolation and critical percolation in two dimensions
• Near-critical percolation in two dimensions
• École d'été de probabilités de Saint-Flour XIV-1984
• On conjectures in first passage percolation theory
• Almost all words are seen in critical site percolation on the triangular lattice
• Nondifferentiability of the time constants of first-passage percolation
• Invasion percolation and the incipient infinite cluster in 2D
• Asymptotics for \(2D\) critical first passage percolation
• Scaling relations for 2D-percolation
• Supercritical behaviors in first-passage percolation
• Hölder regularity and dimension bounds for random curves
• Subdiffusivity of random walk on the 2D invasion percolation cluster
• 50 Years of First-Passage Percolation
• Percolation
• Proof of the Van den Berg–Kesten Conjecture
• Planar lattices do not recover from forest fires

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