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An invariance principle for branching diffusions in bounded domains

Powell, Ellen

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We study branching diffusions in a bounded domain D of Rd in which particles are killed upon hitting the boundary ∂D . It is known that any such process undergoes a phase transition when the branching rate β 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.


Powell, E. (2019). An invariance principle for branching diffusions in bounded domains. Probability Theory and Related Fields, 173(3-4), 999-1062.

Journal Article Type Article
Acceptance Date Apr 16, 2018
Online Publication Date Apr 27, 2018
Publication Date Apr 1, 2019
Deposit Date Sep 28, 2019
Publicly Available Date Sep 22, 2021
Journal Probability Theory and Related Fields
Print ISSN 0178-8051
Electronic ISSN 1432-2064
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 173
Issue 3-4
Pages 999-1062


Accepted Journal Article (968 Kb)

Copyright Statement
This is a post-peer-review, pre-copyedit version of an article published in Probability Theory and Related Fields. The final authenticated version is available online at:

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