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.
Sine-kernel determinant on two large intervals / Fahs, B.; Krasovsky, I.. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - (2024), pp. 1-72. [10.1002/cpa.22147]
Sine-kernel determinant on two large intervals
Krasovsky, I.
2024-01-01
Abstract
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.File in questo prodotto:
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Comm Pure Appl Math - 2023 - Fahs - Sine‐kernel determinant on two large intervals.pdf
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