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arXiv · hep-th/9304063

Level-Spacing Distributions and the Bessel Kernel

Craig A. Tracy·Harold Widom
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Abstract

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 $α$. 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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Craig A. Tracy, Harold Widom. 1999-01-29. Level-Spacing Distributions and the Bessel Kernel. https://doi.org/10.1007/bf02099779

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