Abstract: I discuss the rigid O(n) loop model on planar quadrangulations with so-called Dirichlet-Neumann boundary conditions. From a simple combinatorial decomposition, we are able to find a Wiener-Hopf factorization for the generating functions of the model and to solve it analytically. We also compare our results with those obtained for a similar model on triangulations by Kazakov and Kostov in the physics literature, and to our surprise, find a critical exponent different from the one for triangulations. Time permitting, I will also briefly explain how our results can be generalized to a novel decorated tree model underlying the Dirichlet-Neumann disk structure. Based on a joint work with Jérémie Bouttier (Sorbonne Université) and Grégory Miermont (ENS de Lyon).
Loop-O(n) quadrangulations with mixed boundary conditions
18.04.2024 14:30 - 15:30
Organiser:
M. Lis, W. da Silva
Location:
SR 05, OG 1., OMP 1