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Gap Formation Probability of the $α-$ Ensemble

Yang Chen·Kasper Juel Eriksen
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Abstract

In this paper we employ the continuum approximation of Dyson to determine the asymptotic gap formation probability in the spectrum of $N\times N$ Hermitean random matrices. The associated orthogonal polynomials has weight function, $w(x)=e^{-u(x)},$ where $u(x)=x^α,\;α>0,\;0 1/2$ and depends on $α$ for $0<α<1/2.$

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Yang Chen, Kasper Juel Eriksen. 1994-09-06. Gap Formation Probability of the $α-$ Ensemble. https://doi.org/10.1142/s0217979295000513

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