April 2023 The maximum of branching Brownian motion in Rd
Yujin H. Kim, Eyal Lubetzky, Ofer Zeitouni
Author Affiliations +
Ann. Appl. Probab. 33(2): 1515-1568 (April 2023). DOI: 10.1214/22-AAP1848

Abstract

We show that in branching Brownian motion (BBM) in Rd, d2, the law of Rt, the maximum distance of a particle from the origin at time t, converges as t to the law of a randomly shifted Gumbel random variable.

Funding Statement

Y.K. and E.L. were supported by NSF Grants DMS-1812095 and DMS-2054833. O.Z. was partially supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 692452). This research was further supported in part by BSF Grant 2018088.

Acknowledgements

We thank the referees for a careful reading of the manuscript and useful comments and suggestions.

Citation

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Yujin H. Kim. Eyal Lubetzky. Ofer Zeitouni. "The maximum of branching Brownian motion in Rd." Ann. Appl. Probab. 33 (2) 1515 - 1568, April 2023. https://doi.org/10.1214/22-AAP1848

Information

Received: 1 July 2021; Revised: 1 April 2022; Published: April 2023
First available in Project Euclid: 21 March 2023

zbMATH: 1519.60088
MathSciNet: MR4564433
Digital Object Identifier: 10.1214/22-AAP1848

Subjects:
Primary: 60J65 , 60J70 , 60J80

Keywords: Bessel process , Branching Brownian motion , Extremal process , Log-correlated field

Rights: Copyright © 2023 Institute of Mathematical Statistics

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Vol.33 • No. 2 • April 2023
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