Bernoulli

  • Bernoulli
  • Volume 23, Number 3 (2017), 1784-1821.

Branching random walk with selection at critical rate

Bastien Mallein

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Abstract

We consider a branching-selection particle system on the real line. In this model, the total size of the population at time $n$ is limited by $\exp (an^{1/3})$. At each step $n$, every individual dies while reproducing independently, making children around their current position according to i.i.d. point processes. Only the $\exp (a(n+1)^{1/3})$ rightmost children survive to form the $(n+1)$th generation. This process can be seen as a generalisation of the branching random walk with selection of the $N$ rightmost individuals, introduced by Brunet and Derrida (Phys. Rev. E (3) 56 (1997) 2597–2604). We obtain the asymptotic behaviour of position of the extremal particles alive at time $n$ by coupling this process with a branching random walk with a killing boundary.

Article information

Source
Bernoulli, Volume 23, Number 3 (2017), 1784-1821.

Dates
Received: March 2015
Revised: November 2015
First available in Project Euclid: 17 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1489737625

Digital Object Identifier
doi:10.3150/15-BEJ796

Mathematical Reviews number (MathSciNet)
MR3624878

Zentralblatt MATH identifier
06714319

Keywords
branching random walk selection

Citation

Mallein, Bastien. Branching random walk with selection at critical rate. Bernoulli 23 (2017), no. 3, 1784--1821. doi:10.3150/15-BEJ796. https://projecteuclid.org/euclid.bj/1489737625


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