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Sine-kernel determinant on two large intervals
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DOI：10.1002/cpa.22147.png)
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Abstract
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We consider the probability of two large gaps (intervals without eigenvalues) in the bulk scaling limit of the Gaussian Unitary Ensemble of random matrices. We determine the multiplicative constant in the asymptotics. We also provide the full explicit asymptotics (up to decreasing terms) for the transition between one and two large gaps.
Keywords:
LEVEL-SPACING DISTRIBUTIONS
RIEMANN-HILBERT APPROACH
FREDHOLM DETERMINANTS
DIFFERENTIAL-EQUATIONS
MATRIX MODELS
ASYMPTOTICS
CONSTANT
HANKEL
GAP
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