Comment on "Finite-size scaling of survival probability in branching processes".

Abstract

R. Garcia-Millan etal. [Phys. Rev. E 91, 042122 (2015)PLEEE81539-375510.1103/PhysRevE.91.042122] reported a universal finite-size scaling form of the survival probability in discrete time branching processes. In this comment, we generalize the argument to a wide range of continuous time branching processes. Owing to the continuity, the resulting differential (rather than difference) equations can be solved in closed form, rendering some approximations by R. Garcia-Millan etal. superfluous, although we work along similar lines. In the case of binary branching, our results are in fact exact. Demonstrating that discrete time and continuous time models have their leading order asymptotics in common, raises the question to what extent corrections are identical.