Galton-Watson Branching Process

Offspring distribution: Poisson(μ). Extinction probability q satisfies q = e^{μ(q−1)}. At μ=1 (critical), q=1 but trees can be large.

μ (mean offspring)1.00

Branching tree — generations top to bottom

Click "Grow New Tree"

P(extinction) vs μ — theory (red) and simulation (blue)