Félix Parraud

Asymptotic expansion of smooth functions in deterministic and iid Haar unitary matrices, and application to tensor products of matrices

Let UN be a family of N×N independent Haar unitary random matrices and their adjoints, ZN a family of deterministic matrices, and P a self-adjoint noncommutative polynomial, that is, for any N, P(UN,ZN) is self-adjoint, f a smooth function. We prove that for any k, if f is smooth...