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July 2020 Growth-fragmentation processes in Brownian motion indexed by the Brownian tree
Jean-François Le Gall, Armand Riera
Ann. Probab. 48(4): 1742-1784 (July 2020). DOI: 10.1214/19-AOP1406

Abstract

We consider the model of Brownian motion indexed by the Brownian tree. For every $r\geq 0$ and every connected component of the set of points where Brownian motion is greater than $r$, we define the boundary size of this component, and we then show that the collection of these boundary sizes evolves when $r$ varies like a well-identified growth-fragmentation process. We then prove that the same growth-fragmentation process appears when slicing a Brownian disk at height $r$ and considering the perimeters of the resulting connected components.

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Jean-François Le Gall. Armand Riera. "Growth-fragmentation processes in Brownian motion indexed by the Brownian tree." Ann. Probab. 48 (4) 1742 - 1784, July 2020. https://doi.org/10.1214/19-AOP1406

Information

Received: 1 November 2018; Revised: 1 September 2019; Published: July 2020
First available in Project Euclid: 20 July 2020

zbMATH: 07224959
MathSciNet: MR4124524
Digital Object Identifier: 10.1214/19-AOP1406

Subjects:
Primary: 60J80
Secondary: 60D05, 60J55, 60J65

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 4 • July 2020
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