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

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arxiv 1811.02825 v1 pith:N4NYTBK4 submitted 2018-11-07 math.PR

classification math.PR
keywords browniangrowth-fragmentationmotionboundarycomponentconnectedeveryindexed
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On conditioning a self-similar growth-fragmentation by its intrinsic area

    math.PR 2019-08 conditional novelty 7.0 of 10

    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.

  2. Intrinsic area near the origin for self-similar growth-fragmentations and related random surfaces

    math.PR 2019-08 accept novelty 6.0 of 10

    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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