Coexistence in stochastic spatial models

DOI10.1214/08-AAP590zbMath1178.60069arXiv0906.2293MaRDI QIDQ1024887

Richard T. Durrett

Publication date: 17 June 2009

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

Full work available at URL: https://arxiv.org/abs/0906.2293

zbMATH Keywords

coexistenceopen problemsinteracting particle systemcompetitive exclusion principleblock constructionfast stirring limitmean-field ODEmean-field PDE

Mathematics Subject Classification ID

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

Related Items

Quasi-neutral evolution in populations under small demographic fluctuations ⋮ A stochastic spatial model for the sterile insect control strategy ⋮ The epidemiological consequences of leprosy-tuberculosis co-infection ⋮ Time to absorption for a heterogeneous neutral competition model ⋮ String networks in \(Z_N\) Lotka-Volterra competition models ⋮ Evolutionary graph theory derived from eco-evolutionary dynamics ⋮ Stochastic PDEs on graphs as scaling limits of discrete interacting systems ⋮ Spatial heterogeneity promotes coexistence of rock-paper-scissors metacommunities ⋮ Motion by mean curvature in interacting particle systems ⋮ CHAOTIC COEXISTENCE IN A RESOURCE–CONSUMER MODEL ⋮ Probabilistic Foundations of Spatial Mean-Field Models in Ecology and Applications ⋮ Evolutionary games on the lattice: payoffs affecting birth and death rates

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Are there bushes in a forest?
• A new coexistence result for competing contact processes
• Coexistence in host-pathogen systems
• A simple proof of the stability criterion of Gray and Griffeath
• Flux and fixation in cyclic particle systems
• Rigorous results on mathematical models of catalytic surfaces
• Ergodic theorems for the multitype contact process
• Multicolor particle systems with large threshold and range
• A catalytic surface reaction model
• An extension of a result of grannan and swindle on the poisoning of catalytic surfaces
• Contact interactions on a lattice
• Asymptotic critical value for a competition model
• Particle systems and reaction-diffusion equations
• Coexistence results for catalysts
• The importance of being discrete (and spatial)
• Coexistence results for some competition models
• Spatial aspects of interspecific competition
• Stochastic spatial models of host-pathogen and host-mutualist interactions. I
• Complete convergence theorem for a competition model
• Mutual invadability implies coexistence in spatial models
• Asymptotic Behavior of Excitable Cellular Automata