Category: Statistics

Summary: Testing which survival observables in critical branching depend only on variance and which retain a finite-time sensitivity to offspring skewness.

Critical branching theory predicts that long-time survival depends mainly on the offspring variance, but finite systems can still remember higher moments of the offspring law. This experiment isolates that effect by comparing several critical Galton-Watson processes that all share the same mean and variance while differing in skewness.

The simulation measures both the classic survival tail and conditional observables given survival, such as surviving population size and upper-tail overshoot. The goal is to see whether the rescaled survival probability collapses as theory predicts while the conditioned finite-time observables still vary systematically with skewness.

That distinction matters because many universal laws describe only asymptotic tails. The experiment probes what information about the microscopic offspring distribution remains visible before the asymptotic regime fully takes over.

Method: Repeated critical Galton-Watson simulations with matched mean and variance but varying skewness, run over many independent trials.

What is measured: Survival probability, rescaled survival score, conditional population size, upper-tail overshoot, and dependence on offspring skewness.