# 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}
}
• Published 7 April 2008
• Mathematics
• Constructive Approximation
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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