Determinantal formulae and loop equations

Abstract

We prove that the correlations functions, generated by the determinantal process of the Christoffel-Darboux kernel of an arbitrary order 2 ODE, do satisfy loop equations.

Latex, 35 pages few misprints corrected

References in corpus (7)

• Level-Spacing Distributions and the Airy Kernel
• All genus correlation functions for the hermitian 1-matrix model
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• Higher genus correlators for the hermitian matrix model with multiple cuts
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• Tracy-Widom GUE law and symplectic invariants
• $x-y$ duality in Topological Recursion for exponential variables via Quantum Dilogarithm
• Topological recursion of Eynard-Orantin and the Harmonic Oscillator
• Aspects géométriques et intégrables des modèles de matrices aléatoires
• The asymptotic expansion of Tracy-Widom GUE law and symplectic invariants