Eigenvalues of truncated unitary matrices : disk counting statistics
Let T be an n× n truncation of an (n+ α) × (n+ α) Haar distributed unitary matrix. We consider the disk counting statistics of the eigenvalues of T. We prove that as n→ + ∞ with α fixed, the associated moment generating function enjoys asymptotics of the form exp(C1n+C2+o(1)), where the constants C1 and C2 are given in terms of the incomplete Gamma function. Our proof uses the uniform asymptotics