2020/11/06 by Mohamed Ali Belloum, Belloum, Mohamed Ali, Bastien Mallein +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #60G55 #60G70 #60J80 #92D25 #Analysis of PDEs (math.AP) #Diffusion and Search Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2011.03223
openalex publication_date 2020/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a two-type reducible branching Brownian motion, defined as a particle system on the real line in which particles of two types move according to independent Brownian motion and create offspring at constant rate. Particles of type 1 can give birth to particles of types 1 and 2, but particles of type 2 only give birth to descendants of type 2. Under some specific conditions, Biggins (2012) shows that this process exhibit an anomalous spreading behaviour: the rightmost particle at time t is much further than the expected position for the rightmost particle in a branching Brownian motion consisting only of particles of type 1 or of type 2. This anomalous spreading also has been investigated from a reaction-diffusion equation standpoint by Holzer (2014,2016). The aim of this article is to study the asymptotic behaviour of the position of the furthest particles in the two-type reducible branching Brownian motion, obtaining in particular tight estimates for the median of the maximal displacement.