On an Airy matrix model with a logarithmic potential

Abstract

The Kontsevich-Penner model, an Airy matrix model with a logarithmic potential, may be derived from a simple Gaussian two-matrix model through a duality. In this dual version the Fourier transforms of the n-point correlation functions can be computed in closed form. Using Virasoro constraints, we find that in addition to the parameters $t_n$, which appears in the KdV hierarchies, one needs to introduce here half-integer indices $t_{n/2}$ . The free energy as a function of those parameters may be obtained from these Virasoro constraints. The large N limit follows from the solution to an integral equation. This leads to explicit computations for a number of topological invariants.

35 pages

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• Spectral Form Factor for Time-dependent Matrix model
• Punctures and p-spin curves from matrix models II
• Matrix models for stationary Gromov-Witten invariants of the Riemann sphere
• Punctures and p-spin curves from matrix models
• Random Matrix, Singularities and Open/Close Intersection Numbers
• Punctures and p-spin curves from matrix models III. Dl type and logarithmic potential
• Topological Open/Closed String Dualities: Matrix Models and Wave Functions