First Colonization of a Hard-Edge in Random Matrix Theory

@article{Bertola2008FirstCO,
  title={First Colonization of a Hard-Edge in Random Matrix Theory},
  author={Marco Bertola and S. Y. Lee},
  journal={Constructive Approximation},
  year={2008},
  volume={31},
  pages={231-257}
}
We describe the spectral statistics of the first finite number of eigenvalues in a newly-forming band on the hard-edge of the spectrum of a random Hermitean matrix model, a phenomenon also known as the “birth of a cut” near a hard-edge. It is found that in a suitable scaling regime, they are described by the same spectral statistics of a finite-size Laguerre-type matrix model. The method is rigorously based on the Riemann–Hilbert analysis of the corresponding orthogonal polynomials. 

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