Level-Spacing Distributions and the Bessel Kernel
Tracy, Craig A. ; Widom, Harold
arXiv, 9304063 / Harvested from arXiv
Text on arXiv
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.
Publié le : 1993-04-16
Classification:  High Energy Physics - Theory,  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{9304063,
     author = {Tracy, Craig A. and Widom, Harold},
     title = {Level-Spacing Distributions and the Bessel Kernel},
     journal = {arXiv},
     volume = {1993},
     number = {0},
     year = {1993},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9304063}
}

Tracy, Craig A.; Widom, Harold. Level-Spacing Distributions and the Bessel Kernel. arXiv, Tome 1993 (1993) no. 0, . http://gdmltest.u-ga.fr/item/9304063/