2015/05/19 by Francis Comets, Comets, Francis, Aser Cortines +1
Mathematics · Medicine · #82C22 #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Primary 60K35 #Probability (math.PR) #Secondary 60F17 #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.1505.04971
openalex publication_date 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a particle system studied by E. Brunet and B. Derrida, 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 → ∞. 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.