Gap Formation Probability of the $α-$ Ensemble

Physics – Condensed Matter

Scientific paper

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29, latex

Scientific paper

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 $u(x)=x^{\alpha},\;\alpha>0,\;01/2$ and depends on $\alpha$ for $0<\alpha<1/2.$

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