Matrix integrals as Borel sums of Schur function expansions

Abstract

The partition function for unitary two matrix models is known to be a double KP tau-function, as well as providing solutions to the two dimensional Toda hierarchy. It is shown how it may also be viewed as a Borel sum regularization of divergent sums over products of Schur functions in the two sequences of associated KP flow variables.

PlainTex file. 8 pgs. Based on talk by J. Harnad at the workshop: Symmetry and Perturbation Theory 2002, Cala Gonoone (Sardinia), May 1-26, 2002. To appear in proceedings. (World Scientific, Singapore, eds. S. Abenda, G. Gaeta). Typographical correction made to formula (2.7) to include previously omitted powers of r and x

References in corpus (1)

• Duality, Biorthogonal Polynomials and Multi-Matrix Models

Cited by in corpus (9)

• Fermionic construction of partition functions for two-matrix models and perturbative Schur function expansions
• Scalar products of symmetric functions and matrix integrals
• Tau Functions and Matrix Integrals
• Fermionic construction of partition function for multi-matrix models and multi-component TL hierarchy
• Convolution symmetries of integrable hierarchies, matrix models and τ-functions
• Fermionic approach to the evaluation of integrals of rational symmetric functions
• Hurwitz numbers and matrix integrals labeled with chord diagrams
• Matrix integrals and Hurwitz numbers
• Character expansion of matrix integrals