Summer 2021

Summer Research Project with undergraduate students at Duke University

Students: Andrew Bonafede, Pranay Pherwani

Galton-Watson Processes with Mass 

In this project, we studied branching processes and branching diffusions, which are stochastic (random) processes that model the birth and death of certain organisms (particles). In particular, we study a cell growth model which consists of a continuous time supercritical branching process with an extra parameter(mass). Namely we will assume that the mass of the particles grows according to a deterministic differential equation between the exponentially distributed splitting moments and that in the moment of the division the mass of the particle is divided in a random proportion between k offspring.   The model described above gives an approximation of the biological cell growth process, and it is interesting due to the new mathematical questions that can be analyzed. We read the recent literature in this field and posed and make progress towards new and open problems in this direction.