Electronic Communications in Probability

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

Bastien Mallein

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Branching Brownian motion Brownian motion Branching process

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


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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