## Brazilian Journal of Probability and Statistics

- Braz. J. Probab. Stat.
- Volume 31, Number 3 (2017), 476-501.

### Finite-size corrections to the speed of a branching-selection process

Francis Comets and Aser Cortines

#### Abstract

We consider a particle system studied by E. Brunet and B. Derrida (*Phys. Rev. E* **70** (2004) 016106), which evolves according to a branching mechanism with selection of the fittest keeping the population size fixed and equal to $N$. The particles remain grouped and move like a travelling front driven by a random noise with a deterministic speed. Because of its mean-field structure, the model can be further analysed as $N\to\infty $. We focus on the case where the noise lies in the max-domain of attraction of the Weibull extreme value distribution and show that under mild conditions the correction to the speed has universal features depending on the tail probabilities.

#### Article information

**Source**

Braz. J. Probab. Stat., Volume 31, Number 3 (2017), 476-501.

**Dates**

Received: June 2015

Accepted: October 2016

First available in Project Euclid: 22 August 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1503388825

**Digital Object Identifier**

doi:10.1214/16-BJPS342

**Mathematical Reviews number (MathSciNet)**

MR3693977

**Zentralblatt MATH identifier**

1377.82027

**Keywords**

Front propagation branching random walk selection extreme value theory first-passage percolation finite-size corrections propagation speed mean-field

#### Citation

Comets, Francis; Cortines, Aser. Finite-size corrections to the speed of a branching-selection process. Braz. J. Probab. Stat. 31 (2017), no. 3, 476--501. doi:10.1214/16-BJPS342. https://projecteuclid.org/euclid.bjps/1503388825