Three series of lectures were given at the 32nd Probability Summer School in Saint-Flour
(July 7–24, 2002), by the Professors Pitman, Tsirelson and Werner …

We discuss several connections between discrete and continuous random trees. In the
discrete setting, we focus on Galton-Watson trees under various conditionings. In particular …

We investigate the random continuous trees called Lévy trees, which are obtained as
scaling limits of discrete Galton-Watson trees. We give a mathematically precise definition of …

Consider the minimum spanning tree (MST) of the complete graph with n vertices, when
edges are assigned independent random weights. Endow this tree with the graph distance …

We consider 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 …

Coalescents with multiple collisions, also known as Λ-coalescents, were introduced by
Pitman and Sagitov in 1999. These processes describe the evolution of particles that …

This thesis introduces the alpha model. The alpha model is a one parameter family of
probability models on cladograms (binary leaf-labeled trees) which interpolates …

We survey recent developments about random real trees, whose prototype is the Continuum
Random Tree (CRT) introduced by Aldous in 1991. We briefly explain the formalism of real …

Given any regularly varying dislocation measure, we identify a natural self-similar
fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As …

One major open conjecture in the area of critical random graphs, formulated by statistical
physicists, and supported by a large amount of numerical evidence over the last decade …