Absence of mutual unbounded growth for almost all parameter values in the two-type Richardson model.

DOI10.1016/S0304-4149(00)00042-9zbMath1047.60099WikidataQ126805868 ScholiaQ126805868MaRDI QIDQ1879491

Robin Pemantle, Olle Häggström

Publication date: 22 September 2004

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

zbMATH Keywords

interacting particle systemshape theoremRichardson model

Mathematics Subject Classification ID

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

Related Items (15)

Stochastic Spatial Models of Host-Pathogen and Host-Mutualist Interactions II ⋮ The two-type Richardson model in the half-plane ⋮ Coexistence in chase-escape ⋮ The winner takes it all but one ⋮ Competition in growth and urns ⋮ The two-type Richardson model with unbounded initial configurations ⋮ Coexistence and Noncoexistence of Markovian Viruses and their Hosts ⋮ Coexistence in a two-type continuum growth model ⋮ Survival and coexistence for a multitype contact process ⋮ Competing frogs on \({\mathbb Z}^d\) ⋮ Competing first passage percolation on random regular graphs ⋮ Coexistence of competing first passage percolation on hyperbolic graphs ⋮ Multi-particle diffusion limited aggregation ⋮ Joint Distribution of Distances in Large Random Regular Networks ⋮ Multitype shape theorems for first passage percolation models

Cites Work

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• On the speed of convergence in first-passage percolation
• Some limit theorems for percolation processes with necessary and sufficient conditions
• Ergodic theorems for the multitype contact process
• A note on some rates of convergence in first-passage percolation
• The 1996 Wald memorial lectures. Stochastic models of interacting systems
• Ergodicity of the hard-core model on \(\mathbb{Z}^ 2\) with parity-dependent activities
• First passage percolation: the stationary case
• Concentration of measure and isoperimetric inequalities in product spaces
• The stochastic random-cluster process and the uniqueness of random-cluster measures
• First passage percolation and a model for competing spatial growth

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