Invariant measures of critical spatial branching processes in high dimensions

DOI10.1214/aop/1024404278zbMath0882.60091OpenAlexW1990280691MaRDI QIDQ1356330

Maury Bramson, Andreas Greven, J. Theodore Cox

Publication date: 18 February 1998

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

Full work available at URL: https://doi.org/10.1214/aop/1024404278

zbMATH Keywords

invariant measurescritical branching Brownian motioncritical Dawson-Watanabe process

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (9)

Invariant probability distributions for measure-valued diffusions. ⋮ Multiple scale analysis of clusters in spatial branching models ⋮ Invariant measures of critical branching random walks in high dimension ⋮ Long-time behavior for subcritical measure-valued branching processes with immigration ⋮ The fixed points of branching Brownian motion ⋮ A functional CLT for the occupation time of a state-dependent branching random walk ⋮ Diffraction of stochastic point sets: Explicitly computable examples ⋮ Strong law of large numbers and mixing for the invariant distributions of measure-valued diffusions. ⋮ Clustering and invariant measures for spatial branching models with infinite variance

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• Subadditive mean ergodic theorems
• The critical measure diffusion process
• Ergodic theorems for spatial processes
• Limiting Distributions for Branching Random Fields

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