A shape theorem for the Orthant model

DOI10.1214/20-AOP1476zbMath1487.60183arXiv1911.02615OpenAlexW3151445389MaRDI QIDQ2039431

Thomas S. Salisbury, Mark P. Holmes

Publication date: 2 July 2021

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

Full work available at URL: https://arxiv.org/abs/1911.02615

zbMATH Keywords

random environmentssubadditivityshape theoremOrthant model

Mathematics Subject Classification ID

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

Related Items

The chemical distance in random interlacements in the low-intensity regime, Sharpness of the phase transition for the orthant model

Cites Work

• Unnamed Item
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• Weak shape theorem in first passage percolation with infinite passage times
• Oriented percolation in two dimensions
• An improved subadditive ergodic theorem
• Some limit theorems for percolation processes with necessary and sufficient conditions
• Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment
• On the chemical distance for supercritical Bernoulli percolation
• Lyapunov exponents, shape theorems and large deviations for the random walk in random potential
• Degenerate random environments
• Random Walks in Degenerate Random Environments
• 50 Years of First-Passage Percolation
• On chemical distances and shape theorems in percolation models with long-range correlations
• The supercritical phase of percolation is well behaved
• Asymptotic shape for the chemical distance and first-passage percolation on the infinite Bernoulli cluster
• Phase transitions for degenerate random environments
• Forward Clusters for Degenerate Random Environments