Matrix Integrals, Symmetric Functions theory and matrix integrals
Abstract
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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