Contact and voter processes on the infinite percolation cluster as models of host-symbiont interactions

DOI10.1214/10-AAP734zbMath1234.60093arXiv0911.3107MaRDI QIDQ640054

Fabio Zucca, Nicolas. Lanchier, Daniela Bertacchi

Publication date: 12 October 2011

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

Full work available at URL: https://arxiv.org/abs/0911.3107

zbMATH Keywords

random walksvoter modellogistic growthcontact processmetapopulationbranching random walkssite percolationcomponent communityhostinfracommunityinfrapopulationsymbiont

Mathematics Subject Classification ID

Epidemiology (92D30) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

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Cites Work

• Unnamed Item
• Unnamed Item
• A spatially explicit model for competition among specialists and generalists in a heterogeneous environment
• Coexistence in host-pathogen systems
• Oriented percolation in two dimensions
• A simple proof of the stability criterion of Gray and Griffeath
• On the Williams-Bjerknes tumour growth model. I
• Multicolor particle systems with large threshold and range
• Contact interactions on a lattice
• Ergodic theorems for weakly interacting infinite systems and the voter model
• Random walk on the infinite cluster of the percolation model
• Recurrent graphs where two independent random walks collide finitely often
• Random walks on supercritical percolation clusters
• Isoperimetry and heat kernel decay on percolation clusters.
• Collisions of random walks
• Stochastic spatial models of host-pathogen and host-mutualist interactions. I
• The discrete integral maximum principle and its applications
• Nearest-neighbor Markov interaction processes on multidimensional lattices
• A self-regulating and patch subdivided population
• Stochastic Spatial Models of Host-Pathogen and Host-Mutualist Interactions II
• On the Williams-Bjerknes tumour growth model: II
• Random Walks on Infinite Graphs and Groups
• A model for spatial conflict
• Approximating Critical Parameters of Branching Random Walks
• Probability Inequalities for Sums of Bounded Random Variables