An invariance principle for branching diffusions in bounded domains

Powell, Ellen

doi:10.1007/s00440-018-0847-8

An invariance principle for branching diffusions in bounded domains

Powell, Ellen

Authors

Dr Ellen Powell ellen.g.powell@durham.ac.uk
Associate Professor

Abstract

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.

Citation

Powell, E. (2019). An invariance principle for branching diffusions in bounded domains. Probability Theory and Related Fields, 173(3-4), 999-1062. https://doi.org/10.1007/s00440-018-0847-8

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
DOI	https://doi.org/10.1007/s00440-018-0847-8

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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: https://doi.org/10.1007/s00440-018-0847-8