Category: Statistics

Summary: Testing whether rescaled extinction-time distributions near criticality collapse across different Galton-Watson offspring families.

Branching-process theory predicts universal asymptotic behavior near criticality, but finite distributions can still depend on the microscopic offspring law. This experiment asks whether extinction times in Galton-Watson processes collapse onto a common rescaled curve near the critical window, independent of whether offspring counts are Poisson, geometric, or binomial.

The simulation sweeps across subcritical, critical, and slightly supercritical regimes and measures the full extinction-time distribution, not only its far tail. By comparing higher moments and distribution shape after rescaling, it tests how much universality survives beyond the simplest asymptotic formulas.

That distinction matters because practical branching systems are finite and often operate near, not exactly at, the critical point. The experiment aims to map where universality is accurate and where offspring-family details still remain visible.

Method: Repeated Galton-Watson simulations across the near-critical window, comparing rescaled extinction-time distributions for multiple offspring families.

What is measured: Extinction-time distribution, rescaled distribution collapse, higher moments, tail behavior, and dependence on offspring family.