Exact limiting shape for a simplified model of first-passage percolation on the plane

DOI10.1214/aop/1022855751zbMath0935.60093OpenAlexW2018833576MaRDI QIDQ1307484

Timo Seppäläinen

Publication date: 2 December 1999

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1022855751

zbMATH Keywords

hydrodynamic limitfirst-passage percolationasymptotic shapetagged particle

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43)

Related Items (26)

Hidden invariance of last passage percolation and directed polymers ⋮ A growth model in a random environment ⋮ Large deviations for discrete \(\beta\)-ensembles ⋮ RSK in last passage percolation: a unified approach ⋮ Longest increasing paths with gaps ⋮ From Hammersley's lines to Hammersley's trees ⋮ The random average process and random walk in a space-time random environment in one dimension ⋮ Improved upper bounds on the asymptotic growth velocity of Eden clusters ⋮ Uniform convergence to the Airy line ensemble ⋮ Skew Howe duality and limit shapes of Young diagrams ⋮ Tropical combinatorics and Whittaker functions ⋮ Non-existence of bi-infinite geodesics in the exponential corner growth model ⋮ Estimates for the spreading velocity of an epidemic model. ⋮ Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition ⋮ Thermodynamical approach to the longest common subsequence problem ⋮ Properties of the limit shape for some last-passage growth models in random environments ⋮ On the Markov Transition Kernels for First Passage Percolation on the Ladder ⋮ Limiting shape for directed percolation models ⋮ Random growth models with polygonal shapes ⋮ Order of the variance in the discrete Hammersley process with boundaries ⋮ Fluctuation lower bounds in planar random growth models ⋮ Determinantal transition kernels for some interacting particles on the line ⋮ Existence of hydrodynamics for the totally asymmetric simple \(K\)-exclusion process ⋮ Variational Formula for the Time Constant of First-Passage Percolation ⋮ Batch queues, reversibility and first-passage percolation ⋮ Last passage percolation in an exponential environment with discontinuous rates

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the speed of convergence in first-passage percolation
• Central limit theorems for infinite series of queues and applications to simple exclusion
• The shape of the limit set in Richardson's growth model
• Some limit theorems for percolation processes with necessary and sufficient conditions
• A note on some rates of convergence in first-passage percolation
• First passage percolation for random colorings of \(\mathbb{Z}^ d\)
• Evolution of tagged particles in non-reversible particle systems
• Approximation of subadditive functions and convergence rates in limiting-shape results
• Euclidean models of first-passage percolation
• A limit theorem for the position of a tagged particle in a simple exclusion process
• First passage percolation: the stationary case
• Divergence of shape fluctuations in two dimensions
• Asymptotic shapes for stationary first passage percolation
• A microscopic model for the Burgers equation and longest increasing subsequences
• On Hopf's formulas for solutions of Hamilton-Jacobi equations
• Convex Analysis

This page was built for publication: Exact limiting shape for a simplified model of first-passage percolation on the plane