A complete convergence theorem for voter model perturbations

DOI10.1214/13-AAP919zbMath1291.60202arXiv1210.0830MaRDI QIDQ2443189

J. Theodore Cox, Edwin A. Perkins

Publication date: 4 April 2014

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

Full work available at URL: https://arxiv.org/abs/1210.0830

zbMATH Keywords

interacting particle systemsLotka-Volterra modelvoter model perturbationsannihilating dualscancellative and annihilating processesComplete convergence theoremdual growth conditionstochastic stationary distributionssurvival and coexistence

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Limit theorems in probability theory (60F99)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Coexistence in a two-dimensional Lotka-Volterra model
• Epidemics with recovery in \(D=2\)
• Oriented percolation in two dimensions
• Annihilating branching processes
• Limit theorems for nonergodic set-valued Markov processes
• Additive and cancellative interacting particle systems
• Rescaled contact processes converge to super-Brownian motion in two or more dimensions
• Survival of one-dimensional cellular automata under random perturbations
• Particle systems and reaction-diffusion equations
• Coexistence in threshold voter models
• Domination by product measures
• An explicitly spatial version of the Lotka-Volterra model with interspecific competition
• Rescaled Lotka-Volterra models converge to super-Brownian motion
• The complete convergence theorem for coexistent threshold voter models
• Renormalization of the two-dimensional Lotka-Volterra model
• Voter models with heterozygosity selection
• Survival and coexistence in stochastic spatial Lotka-Volterra models
• Contact processes in several dimensions
• Voter Model Perturbations and Reaction Diffusion Equations