Benedicte Haas (Université Paris-Dauphine)

On scaling limits of Markov branching trees

Probabilists and combinatorists are interested since a long time in the asymptotic description of large random trees, as, for example, large uniform trees (chosen uniformly at random in a certain class of trees) or large conditioned Galton-Watson trees. After recalling classical results on that topic, we will develop the case of a family of random trees satisfying a Markov branching property. Roughly, this property says that the subtrees above some given height are independent with a law that depends only on their total size, the latter being either the number of leaves or vertices. Applications to the description of scaling limits of (1) random uniform unordered trees, (2) growing trees built recursively, (3) Galton-Watson trees will then be discussed.

This talk is based on joint works with Gregory Miermont, Jim Pitman and Matthias Winkel.