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arXiv · 0704.2044

Vertices from replica in a random matrix theory

E. Brezin·S. Hikami
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Abstract

Kontsevitch's work on Airy matrix integrals has led to explicit results for the intersection numbers of the moduli space of curves. In a subsequent work Okounkov rederived these results from the edge behavior of a Gaussian matrix integral. In our work we consider the correlation functions of vertices in a Gaussian random matrix theory, with an external matrix source, in a scaling limit in which the powers of the matrices and their sizes go to infinity simultaneously in a specified scale. We show that the replica method applied to characteristic polynomials of the random matrices, together with a duality exchanging N and the number of points, allows one to recover Kontsevich's results on the intersection numbers, through a simple saddle-point analysis.

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E. Brezin, S. Hikami. 2007-04-16. Vertices from replica in a random matrix theory. https://doi.org/10.1088/1751-8113%2F40%2F45%2F005

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