Convergence to the Brownian CRT for critical branching Markov processe
Abstract
We prove an invariance principle for a general class of continuous time critical branching processes with finite variance (non-local) branching mechanism. We show that the genealogical trees, viewed as random compact metric measure spaces, converge under rescaling to the Brownian continuum random tree in the Gromov-Hausdorff-weak topology, establishing a universal scaling limit for critical finite variance branching processes.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Geometric Analysis and Curvature Flows
advanced mathematical theories
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 9 January 2026
- Document type
- Preprint