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A time-invariant random graph with splitting events

Abstract:

We introduce a process where a connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When a vertex splits, its incoming edges are randomly assigned between its offspring and a Poisson random number of edges are added between them. The process is parametrised by a positive real λ which governs the limiting average degree. We show that for each value of λ there is a unique random connected rooted multigraph $\mathcal{M}$ (λ) invariant un...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1214/21-ecp436

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Institute of Mathematical Statistics Publisher's website
Journal:
Electronic Communications in Probability Journal website
Volume:
26
Pages:
1 - 15
Publication date:
2021-01-06
Acceptance date:
2021-10-29
DOI:
ISSN:
1083-589X
Language:
English
Keywords:
Pubs id:
1224111
Local pid:
pubs:1224111
Deposit date:
2021-12-13

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