Continuity for the asymptotic shape in the frog model with random initial configurations

DOI10.1016/j.spa.2020.04.005zbMath1450.60061OpenAlexW3016668789MaRDI QIDQ2196384

Naoki Kubota

Publication date: 2 September 2020

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2020.04.005

zbMATH Keywords

frog modelrandom environmentsimple random walktime constantasymptotic shapeegg model

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Limit theorems in probability theory (60F99)

Cites Work

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• Sublinear variance in first-passage percolation for general distributions
• The shape theorem for the frog model
• Asymptotic behavior of the Brownian frog model
• First passage time of the frog model has a sublinear variance
• A Hsu-Robbins-Erdős strong law in first-passage percolation
• A zero-one law for recurrence and transience of frog processes
• Large deviations for the chemical distance in supercritical Bernoulli percolation
• Continuity of the time and isoperimetric constants in supercritical percolation
• Lyapunov exponents, shape theorems and large deviations for the random walk in random potential
• The time constant of first-passage percolation on the square lattice
• On the continuity of the time constant of first-passage percolation
• Percolation
• Boundary-connectivity via graph theory
• Deviation bounds for the first passage time in the frog model

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