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Growth-fragmentation processes in Brownian motion indexed by the Brownian tree
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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.
Forward citations
Cited by 2 Pith papers
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On conditioning a self-similar growth-fragmentation by its intrinsic area
The intrinsic area of a self-similar growth-fragmentation has a C-infinity density that decays like r^{-1-omega_+/omega_-}, and this density permits tilting the process to condition on area A=r.
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Intrinsic area near the origin for self-similar growth-fragmentations and related random surfaces
For self-similar growth-fragmentations, the intrinsic area of small root-centered balls has a deterministic almost-sure rate with positive initial size and logarithmic fluctuations when the initial size is zero.
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