@article{8345403b67c2489c85c25fe7055661c0,
title = "1-stable fluctuation of the derivative martingale of branching random walk",
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. (2021) and is the branching random walk counterpart of the main result of Maillard and Pain (2019) for branching Brownian motion.",
keywords = "Branching random walk, Derivative martingale, Spine decomposition",
author = "Haojie Hou and Ren, {Yan Xia} and Renming Song",
note = "The research of this project is supported by the National Key R&D Program of China (No. 2020YFA0712900).The research of this author is supported by NSFC, China (Grant Nos. 12071011 and 12231002) and The Fundamental Research Funds for the Central Universities, China, Peking University LMEQF.Research supported in part by a grant from the Simons Foundation, USA (#960480, Renming Song).We thank the referee for very helpful comments on the first version of this paper. Part of the research for this paper was done while the third-named author was visiting Jiangsu Normal University, where he was partially supported by a grant from the National Natural Science Foundation of China (11931004, Yingchao Xie). The research of this project is supported by the National Key R&D Program of China (No. 2020YFA0712900 ). We thank the referee for very helpful comments on the first version of this paper. Part of the research for this paper was done while the third-named author was visiting Jiangsu Normal University, where he was partially supported by a grant from the National Natural Science Foundation of China ( 11931004 , Yingchao Xie).",
year = "2024",
month = jun,
doi = "10.1016/j.spa.2024.104338",
language = "English (US)",
volume = "172",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier B.V.",
}