Probabilistic approach to a cell growth model

Abstract

We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in random proportion between two offsprings (mitosis). Using the technique of moment equations we study asymptotics of the the mass-space distribution of the particles. Mass distribution of the particles is the solution of the equation with linearly transformed argument: functional, functional-differential or integral. We derive several limit theorems describing the fluctuations of the density of the particles, first two moments of the total masses etc. Also, we consider the branching process in the presence of a random spatial motion (say, diffusion). Here we discuss the classical Fisher, Kolmogorov, Petrovski, Piskunov model and distribution of mass inside the propogation front.