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
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.
Braz. J. Probab. Stat., Volume 31, Number 3 (2017), 476-501.
Received: June 2015
Accepted: October 2016
First available in Project Euclid: 22 August 2017
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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