Growth-fragmentation processes in Brownian motion indexed by the Brownian tree

2018/11/07 by Jean‐François Le Gall, Gall, Jean-François Le, Armand Riera +1
Mathematics · #60D05 #60J80 #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1811.02825

openalex publication_date 2018/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the model of Brownian motion indexed by the Brownian tree. For every r≥ 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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