The smallest eigenvalue distribution of the Unitary Jacobi Ensembles (original) (raw)

In the hard edge scaling limit of the Jacobi unitary ensemble generated by the weight x α (1 − x) β , x ∈ [0, 1], α, β > 0, the probability that all eigenvalues of Hermitian matrices from this ensemble lie in the interval [t, 1] is given by the Fredholm determinant of the Bessel kernel. We derive the constant in the asymptotics of this Bessel-kernel determinant. A specialization of the results gives the constant in the asymptotics of the probability that the interval (−a, a), a > 0, is free of eigenvalues in the Jacobi unitary ensemble with the symmetric weight (1−x 2) β , x ∈ [−1, 1].