Modul:   MAT971  Seminar on Stochastic Processes

Fringe trees for random trees with given vertex degrees

Vortrag von Dr. Gabriel Hernan Berzunza-Ojeda

Sprecher eingeladen von: Prof. Dr. Jean Bertoin

Datum: 27.11.24  Zeit: 17.15 - 18.45  Raum: ETH HG G 43

In this talk, we consider fringe trees of random plane trees with given vertex statistics (i.e., a given number of vertices of each degree). The main results are laws of large numbers and central limit theorems for the number of fringe trees of a given type. The key tool for our proofs is an extension to the multivariate setting of a theorem by Gao and Wormald (2004), which provides a way to show asymptotic normality by analyzing the behaviour of sufficiently high factorial moments. Our results also apply to random simply generated trees (or conditioned Galton–Watson trees) by conditioning on their degree statistic. Joint work with Cecilia Holmgren and Svante Janson (Uppsala University)