Probabilistic approach to a cell growth model

TL;DR

This paper develops a probabilistic framework for analyzing the asymptotic behavior of a supercritical Galton-Watson branching process with mass division, deriving limit theorems for particle mass distribution and fluctuations.

Contribution

It introduces a novel probabilistic approach to model and analyze the mass distribution dynamics in a branching process with random mass division, providing new limit theorems.

Findings

Derived limit theorems for mass distribution fluctuations

Analyzed asymptotic behavior of total particle masses

Solved equations involving functional and integral transforms

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 asymptotic of the mass 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.