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 -> infinity. 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.