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Publication 16-CNA-025
Coagulation And Universal Scaling Limits For Critical Galton-Watson Processes Gautam Iyer Nicholas Leger Robert L. Pego Moreover, our analysis shows that the nonlinear scaling dynamics of CSBPs becomes linear and purely dilatational when expressed in terms of the Lévy triple associated with the branching mechanism. We use this to prove existence of universal critical Galton-Watson and CSBPs analogous to W. Doeblin's "universal laws". Namely, these universal processes generate all possible critical and subcritical CSBPs as subsequential scaling limits. Our convergence results rely on a natural topology for Lévy triples and a continuity theorem for Bernstein transforms (Laplace exponents). We develop these in a self-contained appendix. Get the paper in its entirety as 16-CNA-025.pdf |