Séminaire du 10 mars 03, Gilles Schaeffer, LIX, École polytechnique

Random planar maps, the Ising model and weighted trees.

In a first part I will present a bijection between bipartite maps and some trees, that allows to keep track of black and white vertex degrees. Then I will discuss the Ising model and more generally, properties of random maps that are inherited from random trees by putting weights on vertices. The case of "multi-critical" negative weights raises interesting probabilistic questions.