Rescaled Lotka-Volterra models converge to super-Brownian motion

DOI10.1214/009117904000000973zbMath1078.60082arXivmath/0506591OpenAlexW3103840384MaRDI QIDQ1781171

Edwin A. Perkins, J. Theodore Cox

Publication date: 23 June 2005

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

Full work available at URL: https://arxiv.org/abs/math/0506591

zbMATH Keywords

voter modelspatial competitioncoalescing random walk

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random measures (60G57) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Functional limit theorems; invariance principles (60F17)

Related Items (14)

Survival and coexistence in stochastic spatial Lotka-Volterra models ⋮ Superbrownian motion and the spatial lambda-Fleming-Viot process ⋮ Propagation of chaos and the many-demes limit for weakly interacting diffusions in the sparse regime ⋮ Rescaling the spatial Lambda-Fleming-Viot process and convergence to super-Brownian motion ⋮ Renormalization of the two-dimensional Lotka-Volterra model ⋮ Sharp benefit-to-cost rules for the evolution of cooperation on regular graphs ⋮ Rescaled Lotka-Volterra models converge to super-stable processes ⋮ Large deviations under a viewpoint of metric geometry: measure-valued process cases ⋮ A complete convergence theorem for voter model perturbations ⋮ Coexistence in locally regulated competing populations and survival of branching annihilating random walk ⋮ Voter models with heterozygosity selection ⋮ New large deviation results for some super-Brownian processes ⋮ The dimension of the boundary of super-Brownian motion ⋮ Equivalence of mean-field avalanches and branching diffusions: from the Brownian force model to the super-Brownian motion

Cites Work

• The scaling limit of lattice trees in high dimensions
• Rescaled contact processes converge to super-Brownian motion in two or more dimensions
• An explicitly spatial version of the Lotka-Volterra model with interspecific competition
• Super-Brownian limits of voter model clusters
• Rescaled voter models converge to super-Brownian motion.
• Convergence of critical oriented percolation to super-Brownian motion above \(4+1\) dimensions
• Coexistence in locally regulated competing populations and survival of branching annihilating random walk
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