Differentiability at the edge of the percolation cone and related results in first-passage percolation

DOI10.1007/s00440-012-0425-4zbMath1275.60093arXiv1105.4172OpenAlexW2043227621MaRDI QIDQ1955839

Michael Damron, Antonio Auffinger

Publication date: 19 June 2013

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.4172

zbMATH Keywords

shape fluctuationsoriented percolationfirst-passage percolationRichardson's growth modelgraph of infection

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43)

Related Items (18)

Rate of convergence in first-passage percolation under low moments ⋮ Lower bounds for fluctuations in first-passage percolation for general distributions ⋮ Geodesic length and shifted weights in first-passage percolation ⋮ First passage percolation on \(\mathbb {Z}^2\): a simulation study ⋮ Busemann functions and infinite geodesics in two-dimensional first-passage percolation ⋮ Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman ⋮ Variational formulas and cocycle solutions for directed polymer and percolation models ⋮ Stationary cocycles and Busemann functions for the corner growth model ⋮ Geodesics and the competition interface for the corner growth model ⋮ Limiting geodesics for first-passage percolation on subsets of \(\mathbb{Z}^{2}\) ⋮ Order of the variance in the discrete Hammersley process with boundaries ⋮ Fluctuation lower bounds in planar random growth models ⋮ Flats, spikes and crevices: the evolving shape of the inhomogeneous corner growth model ⋮ Sublinear variance in first-passage percolation for general distributions ⋮ Variational Formula for the Time Constant of First-Passage Percolation ⋮ Random growth models: Shape and convergence rate ⋮ Busemann functions, geodesics, and the competition interface for directed last-passage percolation ⋮ Negative correlation of adjacent Busemann increments

Cites Work

• Central limit theorem for first-passage percolation time across thin cylinders
• On the speed of convergence in first-passage percolation
• Geodesics in first passage percolation
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• The time constant vanishes only on the percolation cone in directed first passage percolation
• Oriented percolation in two dimensions
• The shape of the limit set in Richardson's growth model
• Some limit theorems for percolation processes with necessary and sufficient conditions
• Inequalities for the time constant in first-passage percolation
• Approximation of subadditive functions and convergence rates in limiting-shape results
• Euclidean models of first-passage percolation
• Coexistence for Richardson type competing spatial growth models
• Coexistence in two-type first-passage percolation models
• Strict inequalities for the time constant in first passage percolation.
• Divergence of shape fluctuations in two dimensions
• Asymptotic shapes for stationary first passage percolation
• Examples of nonpolygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models
• Shape fluctuations and random matrices
• Shape of territories in some competing growth models
• Shape fluctuations are different in different directions
• Dynamic Scaling of Growing Interfaces
• Multitype shape theorems for first passage percolation models
• The supercritical phase of percolation is well behaved
• First passage percolation and a model for competing spatial growth
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