A Hsu-Robbins-Erdős strong law in first-passage percolation

DOI10.1214/14-AOP926zbMath1321.60199arXiv1305.6260MaRDI QIDQ2354156

Daniel Ahlberg

Publication date: 10 July 2015

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

Full work available at URL: https://arxiv.org/abs/1305.6260

zbMATH Keywords

large deviationsshape theoremfirst-passage percolationHsu-Robbins-Erdős strong law

Mathematics Subject Classification ID

Strong limit theorems (60F15) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Large deviations (60F10)

Related Items (9)

Rate of convergence in first-passage percolation under low moments ⋮ Speed of convergence in first passage percolation and geodesicity of the average distance ⋮ A variational formula for large deviations in first-passage percolation under tail estimates ⋮ 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 ⋮ Fluctuation lower bounds in planar random growth models ⋮ Deviation bounds for the first passage time in the frog model ⋮ Asymptotics of First-Passage Percolation on One-Dimensional Graphs ⋮ Convergence towards an asymptotic shape in first-passage percolation on cone-like subgraphs of the integer lattice

Cites Work

• On the speed of convergence in first-passage percolation
• On the concentration and the convergence rate with a moment condition in first passage percolation
• On large deviation regimes for random media models
• Some limit theorems for percolation processes with necessary and sufficient conditions
• Large deviations in first-passage percolation
• First passage percolation has sublinear distance variance.
• Concentration of measure and isoperimetric inequalities in product spaces
• Convergence towards an asymptotic shape in first-passage percolation on cone-like subgraphs of the integer lattice
• Large deviations for the chemical distance in supercritical Bernoulli percolation
• On the chemical distance for supercritical Bernoulli percolation
• First-passage percolation, network flows and electrical resistances
• Asymptotics of First-Passage Percolation on One-Dimensional Graphs
• Complete Convergence and the Law of Large Numbers
• On a Theorem of Hsu and Robbins
• Remark on my Paper "On a Theorem of Hsu and Robbins"
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