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arXiv · 1402.1796

Convergence of eigenvalues to the support of the limiting measure in critical $\beta$ matrix models

Chenjie Fan·Alice Guionnet·Yuqi Song·Andi Wang
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Abstract

We consider the convergence of the eigenvalues to the support of the equilibrium measure in the $\beta$ ensemble models under a critical condition. We show a phase transition phenomenon, namely that, with probability one, all eigenvalues will fall in the support of the limiting spectral measure when $\beta>1$, whereas this fails when $\beta<1$.

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Chenjie Fan, Alice Guionnet, Yuqi Song, Andi Wang. 2014-02-07. Convergence of eigenvalues to the support of the limiting measure in critical $\beta$ matrix models. https://arxiv.org/abs/1402.1796

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