Open Access
August 2017 Finite-size corrections to the speed of a branching-selection process
Francis Comets, Aser Cortines
Braz. J. Probab. Stat. 31(3): 476-501 (August 2017). DOI: 10.1214/16-BJPS342


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.


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Francis Comets. Aser Cortines. "Finite-size corrections to the speed of a branching-selection process." Braz. J. Probab. Stat. 31 (3) 476 - 501, August 2017.


Received: 1 June 2015; Accepted: 1 October 2016; Published: August 2017
First available in Project Euclid: 22 August 2017

zbMATH: 1377.82027
MathSciNet: MR3693977
Digital Object Identifier: 10.1214/16-BJPS342

Keywords: Branching random walk , Extreme value theory , finite-size corrections , First-passage percolation , front propagation , mean-field , propagation speed , selection

Rights: Copyright © 2017 Brazilian Statistical Association

Vol.31 • No. 3 • August 2017
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