A Probabilistic Proof for Stable Fluctuations in the Extremal Process of Branching Brownian Motion

Lisa Hartung; Oren Louidor; Tianqi Wu

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arXiv · 2504.21455

A Probabilistic Proof for Stable Fluctuations in the Extremal Process of Branching Brownian Motion

Lisa Hartung·Oren Louidor·Tianqi Wu

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Abstract

We give a probabilistic proof for the emergence of the Stable-$1$ Law for the random fluctuations of the mass of the extremal process of branching Brownian Motion away from its tip. This result was already shown by Mytnik et al. albeit using PDE techniques. As a consequence, we demystify the origin of these fluctuations and the meaning of the deterministic centering function required.

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Lisa Hartung, Oren Louidor, Tianqi Wu. 2025-04-30. A Probabilistic Proof for Stable Fluctuations in the Extremal Process of Branching Brownian Motion. https://arxiv.org/abs/2504.21455

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