Sine‐kernel determinant on two large intervals
Benjamin Fahs, Igor Krasovsky
Abstract
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.
Topics & Concepts
MathematicsMultiplicative functionSineEigenvalues and eigenvectorsGaussianScalingUnitary stateConstant (computer programming)Kernel (algebra)Limit (mathematics)Scaling limitRandom matrixMathematical analysisCircular ensembleStatistical physicsPure mathematicsQuantum mechanicsGeometryPhysicsPolitical scienceComputer scienceProgramming languageLawRandom Matrices and ApplicationsStochastic processes and statistical mechanicsBayesian Methods and Mixture Models