Matrix Integrals, Symmetric Functions theory and matrix integrals

Details Matrix Integrals, Symmetric Functions theory and matrix integrals Matrix Integrals, Symmetric Functions theory and matrix integrals

2002-07-17

arxiv.org/abs/nlin/0207030v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Latex, 59 pages, no figures

Scientific paper

We consider certain scalar product of symmetric functions which is parameterized by a function $r$ and an integer $n$. One the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of this product with the help of multi-integrals. This gives links between a theory of symmetric functions, soliton theory and models of random matrices (such as a model of normal matrices).

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