An introduction to Galton-Watson trees and their local limits

Abstract

The aim of this lecture is to give an overview of old and new resultson Bienaymé-Galton-Watson (BGW) trees. After introducing the framework of discretetrees, we first give alternative proofs of classical results on theextinction probability of BGW processes and on thedescription of the processes conditioned on extinction or onnon-extinction. Then, we study recent local limits of critical orsub-critical BGW trees conditioned to be large.

Lecture given in Hammamet, December 2014

References in corpus (4)

• Condensation in nongeneric trees
• Conditioning Galton-Watson trees on large maximal out-degree
• Local convergence of critical random trees and continuous-state branching processes
• A note on the maximal out-degree of Galton-Watson trees

Cited by in corpus (3)

• Level-set percolation for the Gaussian free field on a transient tree
• Enumeration of fully parked trees
• Ergodic theorem for branching Markov chains indexed by trees with arbitrary shape