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10 papers · 2 filters
Planar maps and random partitions
Jérémie Bouttier
This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter…
Topological Recursion, Airy structures in the space of cycles
B Eynard
Topological recursion associates to a spectral curve, a sequence of meromorphic differential forms. A tangent space to the "moduli space" of spectral curves (its space of deformati…
Bond percolation thresholds on Archimedean lattices from critical polynomial roots
Christian R. Scullard, Jesper Lykke Jacobsen
We present percolation thresholds calculated numerically with the eigenvalue formulation of the method of critical polynomials; developed in the last few years, it has already prov…
Arctic curves of the twenty-vertex model with domain wall boundaries
Bryan Debin, Philippe Di Francesco, Emmanuel Guitter
We use the tangent method to compute the arctic curve of the Twenty-Vertex (20V) model with particular domain wall boundary conditions for a wide set of integrable weights. To this…
Solutions of loop equations are random matrices
B. Eynard
For a given polynomial , a random matrix eigenvalues measure is a measure on . Hermiti…
From the quantum geometry of Fuchsian systems to conformal blocks of W-algebras
Raphaël Belliard, Bertrand Eynard
We consider the moduli space of holomorphic principal bundles for reductive Lie groups over Riemann surfaces (possibly with boundaries) and equipped with meromorphic connections. W…