We extend the relation between random matrices and free probability theory from the level of expectations to the level of all correlation functions (which are classical cumulants of traces of… (More)

Many high contrast coronagraph designs have recently been proposed. In this paper, their suitability for direct imaging of extrasolar terrestrial planets is reviewed. We also develop a linearalgebra… (More)

We give a Fourier-type formula for computing the orthogonal Weingarten formula. The Weingarten calculus was introduced as a systematic method to compute integrals of polyno-mials with respect to Haar… (More)

This paper is the first of a series where we study quantum channels from the random matrix point of view. We develop a graphical tool that allows us to compute the expected moments of the output of a… (More)

In this paper, we present applications of the calculus developed in [9], and obtain an exact formula for the moments of random quantum channels whose input is a pure state thanks to gaussianization… (More)

Abstract. We study random vectors of the form (Tr(AV ), . . . , Tr(AV )), where V is a uniformly distributed element of a matrix version of a classical compact symmetric space, and the A are… (More)

We show that Connes’ embedding problem for II1-factors is equivalent to a statement about distributions of sums of self-adjoint operators with matrix coefficients. This is an application of a… (More)

In this paper, we prove that in small parameter regions, arbitrary unitary matrix integrals converge in the large N limit and match their formal expansion. Secondly we give a combinatorial model for… (More)

We study the liberation process for projections: (p, q) 7→ (pt, q) = (utput , q) where ut is a free unitary Brownian motion freely independent from {p, q}. Its action on the operator-valued angle… (More)