Journée "Cartes Aléatoires"

Limite locale des cartes cFK via la bijection Hamburger-Cheesburger

by Prof. Linxiao CHEN (Université Paris-Sud, Orsay)

Centre de conférences Marilyn et James Simons (I.H.E.S.)

Centre de conférences Marilyn et James Simons


Le Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette

We investigate how deeply nested are the loops in the O(n) model on random maps. In particular, we find that the number P of loops separating two points in a planar map in the dense phase with V >> 1 vertices is typically of order c(n) \ln V for a universal constant c(n), and we compute the large deviations of P. The formula we obtain shows similarity to the CLE_{\kappa} nesting properties for n = 2\cos\pi(1 - 4/\kappa). The results can be extended to all topologies using the topological recursion.

This is based on a joint ongoing work with J. Bouttier