Electronic Communications in Probability

Maximal displacement in the $d$-dimensional branching Brownian motion

Bastien Mallein

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Abstract

We consider a branching Brownian motion evolving in $\mathbb{R}^d$. We prove that the asymptotic behaviour of the maximal displacement is given by a first ballistic order, plus a logarithmic correction that increases with the dimension $d$. The proof is based on simple geometrical evidence. It leads to the interesting following side result: with high probability, for any $d \geq 2$, individuals on the frontier of the process are close parents if and only if they are geographically close.

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 76, 12 pp.

Dates
Accepted: 24 October 2015
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465321003

Digital Object Identifier
doi:10.1214/ECP.v20-4216

Mathematical Reviews number (MathSciNet)
MR3417448

Zentralblatt MATH identifier
1329.60307

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60J70 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Branching Brownian motion Brownian motion Branching process

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Mallein, Bastien. Maximal displacement in the $d$-dimensional branching Brownian motion. Electron. Commun. Probab. 20 (2015), paper no. 76, 12 pp. doi:10.1214/ECP.v20-4216. https://projecteuclid.org/euclid.ecp/1465321003


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