The set NC(n) of noncrossing partitions of {1, . . . , n} has been studied as an important example of a lattice, at least since the work of Kreweras [14]. It is customary (also since [14]) to draw… (More)

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)

We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We introduce the concept of “second order freeness” and… (More)

Let ? 2n be the set of paths with 2n steps of unit length in Z 2 , which begin and end at (0; 0). For 2 ? 2n , let area() 2 Z denote the oriented area enclosed by. We show that for every positive… (More)

We consider settings where the observations are drawn from a zero-mean multivariate (real or complex) normal distribution with the population covariance matrix having eigenvalues of arbitrary… (More)

In this paper we establish a connection between the fluctuations of Wishart random matrices, shifted Chebyshev polynomials, and planar diagrams whose linear span form a basis for the irreducible… (More)

The main theorem is that if A is a C*-algebra with a countable approximate identity consisting of projections, then the unitary group of M(A ® K) is contractible. This gives a realization, via the… (More)

The asymptotic behavior of the eigenvalues of a sample covariance matrix is described when the observations are from a zero mean multivariate (real or complex) normal distribution whose covariance… (More)

Let A θ be the rotation C*-algebra for angle θ. For θ = p/q with p and q relatively prime, A θ is the sub-C*-algebra of Mq(C(T 2)) generated by a pair of unitaries u and v satisfying uv = e 2πiθ vu.… (More)