Random planar maps coupled to spin systems

Linxiao CHEN

IPhT et Lab. Mathématiques d'Orsay

Mon, Apr. 16th 2018, 10:00

(voir dans annonce),

Planar maps are essentially graphs embedded in the plane. They have a very rich combinatorial structure and a deep relation to algebra. Random planar maps provide a natural discrete model for two-dimensional random geometry, and their study is motivated in particular by the theory of Liouville quantum gravity. The aim of this thesis is to improve our understanding of random planar maps when their distributions are coupled to a statistical physics model, which is a natural setting for quantum gravity. \par The presentation will focus on two closely related particular models of such random planar maps. The first model consists of random quadrangulations coupled to an O(n)-loop model. After completing the proof of its phase diagram, we concentrate on the non-generic critical phase and show that the lengths and the nesting structure of the loops converge to an multiplicative cascade. Then we turn to a model of Ising-coupled random triangulations. We construct its local limit under Dobrushin boundary condition using the explicit solution of its partition function and a peeling process. \\ \\ (Will be held in: Université Paris-Sud, bâtiment 307, salle 2L8.)

Contact : lbervas