An invariance principle for branching diffusions in bounded domains

DOI10.1007/S00440-018-0847-8zbMATH Open1411.60118arXiv1512.00031OpenAlexW2507910249MaRDI QIDQ1740592

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Publication date: 30 April 2019

Published in: (Search for Journal in Brave)

Abstract: We study branching diffusions in a bounded domain $D$ of $mathbb{R}^d$ in which particles are killed upon hitting the boundary $partialD$. It is known that any such process undergoes a phase transition when the branching rate $$ exceeds a critical value: a multiple of the first eigenvalue of the generator of the diffusion. We investigate the system at criticality and show that the associated genealogical tree, when the process is conditioned to survive for a long time, converges to Aldous' Continuum Random Tree under appropriate rescaling. The result holds under only a mild assumption on the domain, and is valid for all branching mechanisms with finite variance, and a general class of diffusions.

Full work available at URL: https://arxiv.org/abs/1512.00031

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