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July 2019 The structure of extreme level sets in branching Brownian motion
Aser Cortines, Lisa Hartung, Oren Louidor
Ann. Probab. 47(4): 2257-2302 (July 2019). DOI: 10.1214/18-AOP1308

Abstract

We study the structure of extreme level sets of a standard one-dimensional branching Brownian motion, namely the sets of particles whose height is within a fixed distance from the order of the global maximum. It is well known that such particles congregate at large times in clusters of order-one genealogical diameter around local maxima which form a Cox process in the limit. We add to these results by finding the asymptotic size of extreme level sets and the typical height of the local maxima whose clusters carry such level sets. We also find the right tail decay of the distribution of the distance between the two highest particles. These results confirm two conjectures of Brunet and Derrida (J. Stat. Phys. 143 (2011) 420–446). The proofs rely on a careful study of the cluster distribution.

Citation

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Aser Cortines. Lisa Hartung. Oren Louidor. "The structure of extreme level sets in branching Brownian motion." Ann. Probab. 47 (4) 2257 - 2302, July 2019. https://doi.org/10.1214/18-AOP1308

Information

Received: 1 April 2017; Revised: 1 August 2018; Published: July 2019
First available in Project Euclid: 4 July 2019

zbMATH: 07114717
MathSciNet: MR3980921
Digital Object Identifier: 10.1214/18-AOP1308

Subjects:
Primary: 60G70, 60J80
Secondary: 60G15

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 4 • July 2019
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