Dear Colleagues,

We would like to invite you to the following SPASS seminar (joint organised by UniPi, SNS, UniFi and UniSi):

A Limit Theorem for the Total Progeny Distribution of Multitype Branching Processes

by Ivan Kryven (Utrecht University).

The seminar will take place in person on Friday 23rd January at 10:00 in Aula Tricerri, Department of Mathematics and Computer Science, University of Florence. It will be also streamed online here:
https://meet.google.com/boc-aphg-bbk

On behalf of the organisers,
Elia Bisi

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Abstract:
Multitype branching processes model random trees whose vertices carry types, with each vertex producing offspring according to a type‑dependent multivariate distribution. In this talk, I will present a limit theorem describing the behavior of such processes in the noncritical regime. Specifically, we show that the relative frequencies of the different types in any finite realization converge to a deterministic vector, and that the distribution of the total progeny exhibits exponential decay.
These results require only that all moments of the offspring distribution exist. The proof combines several analytic tools, including the Lagrange–Good and arborescent Lagrange inversion formulas, a measure‑tilting argument, and a local limit theorem. I will also discuss applications to models such as random graphs and multi‑component coagulation processes.
Joint work with Jochem Hoogendijk and Rik Versendaal.