Level Spacing Distributions and the Bessel Kernel

@inproceedings{Tracy1993LevelSD,
  title={Level Spacing Distributions and the Bessel Kernel},
  author={Craig A. Tracy and Harold Widom},
  year={1993}
}
Scaling models of random N ×N hermitian matrices and passing to the limit N → ∞ leads to integral operators whose Fredholm determinants describe the statistics of the spacing of the eigenvalues of hermitian matrices of large order. For the Gaussian Unitary Ensemble, and for many others as well, the kernel one obtains by scaling in the “bulk” of the spectrum is the “sine kernel” sin π(x−y) π(x−y) . Rescaling the GUE at the “edge” of the spectrum leads to the kernel Ai(x)Ai ′(y)−Ai′(x) Ai(y) x−y… CONTINUE READING
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