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

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• Borot, G (Max-Planck-Institut fur Mathematik, Bonn)
• Wednesday 22 April 2015, 11:30-12:30
• Seminar Room 1, Newton Institute.

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Random Geometry

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 = 2spi(1 - 4/kappa). The results can be extended to all topologies using the methods of topological recursion.

This talk is part of the Isaac Newton Institute Seminar Series series.

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