Infinite rate mutually catalytic branching in infinitely many colonies: the longtime behavior

DOI10.1214/10-AOP621zbMath1244.60088arXiv0910.4120MaRDI QIDQ662425

Leonid Mytnik, Achim Klenke

Publication date: 22 February 2012

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

Full work available at URL: https://arxiv.org/abs/0910.4120

zbMATH Keywords

stochastic differential equationsLévy noisemutually catalytic branchingcoexistence of typessegregation of typesTrotter product

Mathematics Subject Classification ID

Brownian motion (60J65) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Sample path properties (60G17) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Local time and additive functionals (60J55)

Related Items (8)

The scaling limit of the interface of the continuous-space symbiotic branching model ⋮ Longtime Behavior for Mutually Catalytic Branching with Negative Correlations ⋮ Infinite rate symbiotic branching on the real line: the tired frogs model ⋮ Infinite rate mutually catalytic branching in infinitely many colonies: construction, characterization and convergence ⋮ On the moments and the interface of the symbiotic branching model ⋮ A Trotter-type approach to infinite rate mutually catalytic branching ⋮ Infinite rate mutually catalytic branching ⋮ A new look at duality for the symbiotic branching model

Cites Work

• A Trotter-type approach to infinite rate mutually catalytic branching
• Infinite rate mutually catalytic branching
• Convergence to genetically uniform state in stepping stone models of population genetics
• An interacting system in population genetics. I
• Ergodic theorems for weakly interacting infinite systems and the voter model
• Long-time behavior and coexistence in a mutually catalytic branching model
• Ergodic theorems for infinite systems of locally interacting diffusions
• Infinite rate mutually catalytic branching in infinitely many colonies: construction, characterization and convergence
• Critical dimension for a model of branching in a random medium
• Generalized potlatch and smoothing processes
• Stability of Critical Cluster Fields
• A model for spatial conflict
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Infinite rate mutually catalytic branching in infinitely many colonies: the longtime behavior