The smallest eigenvalue distribution of the Jacobi unitary ensembles

In the hard edge scaling limit of Jacobi unitary ensemble generated by weight xα(1 − x)β, x ∈ [0, 1], α, β > −1, probability that all eigenvalues Hermitian matrices from this lie in interval [t, 1] is given Fredholm determinant Bessel kernel. We derive constant asymptotics kernel determinant. A specialization results gives (− a, a), a 0 free with symmetric (1 x2)β, [− 1, 1].