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An Isaac Newton Institute Workshop

Recent Perspectives in Random Matrix Theory and Number Theory

Spacing distributions for random matrix ensembles

Author: Peter Forrester (University of Melbourne)

Abstract

The calculation of eigenvalue spacing distributions for classical random matrix ensembles with unitary symmetry is intimately related to the theory of integrable systems and Painleve' equations. These theories provide the characterization of spacing distributions as solutions of nonlinear equations solvable in terms of Painleve' transcendents. Two approaches to achieve this goal will be detailed. One approach makes use of function theoretic properties of Fredholm determinants. The other proceeds via the theory of Painleve' systems.

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