Abstract
In this paper we study the maximal position process of branching Brownian motion in random spatial environment. The random environment is given by a process satisfying certain conditions. We show that the maximum position of particles alive at time t satisfies a quenched strong law of large numbers and an annealed invariance principle.
Funding Statement
The research of this project is supported by the National Key R&D Program of China (No. 2020YFA0712900). Yan-Xia Ren’s research is partially supported by NSFC (Grant Nos. 11731009, 12071011 and 12231002) and LMEQF. Renming Song’s research is partially supported by the Simons Foundation (#960480, Renming Song).
Acknowledgments
We thank the referee for helpful comments and suggestions 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) and by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
Citation
Haojie Hou. Yan-Xia Ren. Renming Song. "Invariance principle for the maximal position process of branching Brownian motion in random environment." Electron. J. Probab. 28 1 - 63, 2023. https://doi.org/10.1214/23-EJP956
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