Supercritical branching processes are intimately connected to nuclear fission. Thus, understanding the long-term behaviour of the former can be useful for understanding the latter. The first order behaviour of supercritical branching processes is well understood either through the asymptotic behaviour of the first moment of the process or laws of large numbers type results. However, the second order behaviour is imperative for understanding the fluctuations around the average behaviour and the rate of convergence of the process. In this project, we look at three regimes and characterise these fluctuations via a series of functional central limit theorems.

Project team: Emma Horton, Christopher Dean