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arXiv · 1108.1958

On an Airy matrix model with a logarithmic potential

E. Brezin·S. Hikami
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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.

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E. Brezin, S. Hikami. 2011-08-09. On an Airy matrix model with a logarithmic potential. https://doi.org/10.1088/1751-8113/45/4/045203

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