114 citations · 274 across the 5 of their papers we have counts for
7 papers · 1 filter
Second Order Cumulants of products
James A. Mingo, Roland Speicher, Edward Tan
We derive a formula which expresses a second order cumulant whose entries are products as a sum of cumulants where the entries are single factors. This extends to the second order…
On the Characteristic Polynomial of the Almost Mathieu Operator
Michael P. Lamoureux, James A. Mingo
Let theta = p/q with p and q relatively prime and u and v a pair of unitaries such that u v = e^{i theta} v u, where u and v generate the rotation C*-algebra A_theta. Let h_{theta,…
Second Order Freeness and Fluctuations of Random Matrices, III. Higher order freeness and free cumulants
Benoit Collins, James A. Mingo, Piotr Sniady +1
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 o…
Orthogonal Polynomials and Fluctuations of Random Matrices
Timothy Kusalik, James A. Mingo, Roland Speicher
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 t…
Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices
James A. Mingo, Piotr Sniady, Roland Speicher
We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We show how the concept of "second order fre…
Second Order Freeness and Fluctuations of Random Matrices: I. Gaussian and Wishart matrices and Cyclic Fock spaces
James A. Mingo, Roland Speicher
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 fr…