Level-Spacing Distributions and the Bessel Kernel

Details Level-Spacing Distributions and the Bessel Kernel Level-Spacing Distributions and the Bessel Kernel

1993-04-16

arxiv.org/abs/hep-th/9304063v2

Commun.Math.Phys. 161 (1994) 289-310

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, resubmitted to make postscript compatible, no changes to manuscript content

Scientific paper

10.1007/BF02099779

The level spacing distributions which arise when one rescales the Laguerre or Jacobi ensembles of hermitian matrices is studied. These distributions are expressible in terms of a Fredholm determinant of an integral operator whose kernel is expressible in terms of Bessel functions of order $\alpha$. We derive a system of partial differential equations associated with the logarithmic derivative of this Fredholm determinant when the underlying domain is a union of intervals. In the case of a single interval this Fredholm determinant is a Painleve tau function.

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