Stochastic Flows and Marked Stable Processes

Elie Aïdékon; Quan Shi; Chengshi Wang

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arXiv · 2512.05466

Stochastic Flows and Marked Stable Processes

Elie Aïdékon·Quan Shi·Chengshi Wang

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Abstract

We construct a random partition of the space-time plane $\mathbb{R}_+\times \mathbb{R}$ using two coupled stochastic squared Bessel flows, whose parameters differ by $\delta\in (0,2)$. We show that the cells of this partition correspond to squared Bessel excursions with a negative parameter $-\delta$ which are embedded within the jumps of a spectrally positive $(1+\frac\delta 2)$ stable process. In particular, we demonstrate that interval partition evolutions [Forman et. al. 2020] and stable shredded disks [Bj\"ornberg, Curien and Stef\'ansson 2022] arise naturally in this framework.

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Elie Aïdékon, Quan Shi, Chengshi Wang. 2025-12-05. Stochastic Flows and Marked Stable Processes. https://arxiv.org/abs/2512.05466

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