Mesoscopic colonization of a spectral band

@article{Bertola2009MesoscopicCO,
  title={Mesoscopic colonization of a spectral band},
  author={Marco Bertola and S. Y. Lee and M. Y. Mo},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2009},
  volume={42},
  pages={415204}
}
We consider the unitary matrix model in the limit where the size of the matrices becomes infinite and in the critical situation when a new spectral band is about to emerge. In previous works, the number of expected eigenvalues in the neighborhood of the band was fixed and finite, a situation that was termed ‘birth of a cut’ or ‘first colonization’. We now consider the transitional regime where this microscopic population in the new band grows without bounds but at a slower rate than the size of… 

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