Brazilian Journal of Probability and Statistics

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

Francis Comets and Aser Cortines

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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

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


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.

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