Approximation of subadditive functions and convergence rates in limiting-shape results

DOI10.1214/aop/1024404277zbMath0882.60090OpenAlexW1988095690MaRDI QIDQ1356329

Kenneth S. Alexander

Publication date: 12 March 1998

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

Full work available at URL: https://doi.org/10.1214/aop/1024404277

zbMATH Keywords

connectivity functionsubadditivitylongest common subsequencefirst-passage percolationoriented first-passage percolation

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Combinatorial probability (60C05) Percolation (82B43) Rate of convergence, degree of approximation (41A25)

Related Items (35)

Power-law corrections to exponential decay of connectivities and correlations in lattice models. ⋮ Ornstein-Zernike theory for the Bernoulli bond percolation on \(\mathbb Z^d\) ⋮ A growth model in a random environment ⋮ Divergence of non-random fluctuation for Euclidean first-passage percolation ⋮ The size of the boundary in first-passage percolation ⋮ Rate of convergence in first-passage percolation under low moments ⋮ Fluctuations of transverse increments in two-dimensional first passage percolation ⋮ Speed of convergence in first passage percolation and geodesicity of the average distance ⋮ A near-optimal rate of periodic homogenization for convex Hamilton-Jacobi equations ⋮ Central limit theorem for first-passage percolation time across thin cylinders ⋮ Localization for random walks among random obstacles in a single Euclidean ball ⋮ Increasing sequences of independent points on the planar lattice ⋮ Divergence of shape fluctuation for general distributions in first-passage percolation ⋮ Lower bounds for fluctuations in first-passage percolation for general distributions ⋮ Rate of convergence of the mean for sub-additive ergodic sequences ⋮ Optimal tail exponents in general last passage percolation via bootstrapping \& geodesic geometry ⋮ Quantitative stochastic homogenization of the G equation ⋮ On the rate of convergence in homogenization of time-fractional Hamilton-Jacobi equations ⋮ Uniform fluctuation and wandering bounds in first passage percolation ⋮ The rate of the convergence of the mean score in random sequence comparison ⋮ Lower bounds for boundary roughness for droplets in Bernoulli percolation ⋮ Busemann functions and infinite geodesics in two-dimensional first-passage percolation ⋮ Differentiability at the edge of the percolation cone and related results in first-passage percolation ⋮ A simplified proof of the relation between scaling exponents in first-passage percolation ⋮ Sparse long blocks and the micro-structure of the longuest common subsequences ⋮ Large deviations for global maxima of independent superadditive processes with negative drift and an application to optimal sequence alignments ⋮ Random growth models with polygonal shapes ⋮ Fluctuation lower bounds in planar random growth models ⋮ Directed polymer in random environment and last passage percolation ⋮ Directed polymers in a random environment: Some results on fluctuations ⋮ Random growth models: Shape and convergence rate ⋮ A general method for lower bounds on fluctuations of random variables ⋮ Divergence of non-random fluctuation in first passage percolation ⋮ Exact limiting shape for a simplified model of first-passage percolation on the plane ⋮ Fluctuation estimates for the multi-cell formula in stochastic homogenization of partitions

Cites Work

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• Gaussian fluctuations of connectivities in the subcritical regime of percolation
• On the speed of convergence in first-passage percolation
• The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation
• 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 on the square lattice
• Some limit results for longest common subsequences
• A phase transition for the score in matching random sequences allowing deletions
• The rate of convergence of the mean length of the longest common subsequence
• Weighted sums of certain dependent random variables
• Lower bounds on the connectivity function in all directions for Bernoulli percolation in two and three dimensions
• Ergodicity of the 2D Navier-Stokes equations with random forcing

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