Department of Mathematics
Level-Spacing Distributions and the Bessel Kernel
- Author(s): Tracy, Craig A.
- Widom, Harold
- et al.
Published Web Locationhttps://arxiv.org/pdf/hep-th/9304063.pdf
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.