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

Published 28 Nov 2023 in math.PR | (2311.16407v1)

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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