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arXiv · 2311.16407

$1$-stable fluctuation of the derivative martingale of branching random walk

Haojie Hou·Yan-Xia Ren·Renming Song
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Abstract

In this paper, we study the functional convergence in law of the fluctuations of the derivative martingale of branching random walk on the real line. Our main result strengthens the results of Buraczewski et. al. [Ann. Probab., 2021] and is the branching random walk counterpart of the main result of Maillard and Pain [Ann. Probab., 2019] for branching Brownian motion.

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Haojie Hou, Yan-Xia Ren, Renming Song. 2023-11-28. $1$-stable fluctuation of the derivative martingale of branching random walk. https://arxiv.org/abs/2311.16407

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