Double Scaling Limit in Random Matrix Models and a Nonlinear Hierarchy of Differential Equations

Abstract

We derive the double scaling limit of eigenvalue correlations in the random matrix model at critical points and we relate the limiting correlation functions to a nonlinear hierarchy of ordinary differential equations.

17 pages, latex, J. Phys. A special issue on random matrices

References in corpus (1)

• Eigenvalue correlations on Hyperelliptic Riemann surfaces

Cited by in corpus (10)

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• Phase transitions for deformations of JT supergravity and matrix models
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• Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation
• Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies
• Double scaling limits of random matrices and minimal (2m,1) models: the merging of two cuts in a degenerate case
• Large N expansions and Painlevé hierarchies in the Hermitian matrix model