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Nesting statistics in the O(n) loop model on random lattices

Presented by: 
G Borot Max-Planck-Institut fur Mathematik, Bonn
Wednesday 22nd April 2015 - 11:30 to 12:30
INI Seminar Room 1
Co-author: Jeremie Bouttier (CEA Saclay and ENS Paris)

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 methods of topological recursion.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons