Results 11 to 20 of about 460 (26)

Rectangular R-transform as the limit of rectangular spherical integrals [PDF]

, 2011
In this paper, we connect rectangular free probability theory and spherical integrals. In this way, we prove the analogue, for rectangular or square non-Hermitian matrices, of a result that Guionnet and Maida proved for Hermitian matrices in 2005.
Benaych-Georges, Florent
core   +3 more sources

Large N limit of the Yang–Mills measure on compact surfaces II: Makeenko–Migdal equations and the planar master field

Forum of Mathematics, Sigma
This paper considers the large N limit of Wilson loops for the two-dimensional Euclidean Yang–Mills measure on all orientable compact surfaces of genus larger or equal to $1$ , with a structure group given by a classical compact matrix Lie group ...
Antoine Dahlqvist, Thibaut Lemoine
doaj   +1 more source

Faithfulness of bi-free product states

, 2018
Given a non-trivial family of pairs of faces of unital C*-algebras where each pair has a faithful state, it is proved that if the bi-free product state is faithful on the reduced bi-free product of this family of pairs of faces then each pair of faces ...
Ramsey, Christopher
core   +1 more source

The simplex of tracial quantum symmetric states

, 2014
We show that the space of tracial quantum symmetric states of an arbitrary unital C*-algebra is a Choquet simplex and is a face of the tracial state space of the universal unital C*-algebra free product of A with itself infinitely many times.
Dabrowski, Yoann, Dykema, Kenneth J., Mukherjee, Kunal   +2 more
core   +2 more sources

On the first continuous $L^2$-cohomology of free group factors

, 2014
We prove that the first continuous $L^2$-cohomology of free group factors vanishes. This answers a question by Andreas Thom regarding continuity properties of free difference quotients and shows that one can not distinguish free group factors by means of
Alekseev, Vadim
core   +1 more source

Perturbations of diagonal matrices by band random matrices [PDF]

, 2011
We exhibit an explicit formula for the spectral density of a (large) random matrix which is a diagonal matrix whose spectral density converges, perturbated by the addition of a symmetric matrix with Gaussian entries and a given (small) limiting variance ...
Benaych-Georges, Florent, Enriquez, Nathanaël   +1 more
core   +3 more sources

On a surprising relation between rectangular and square free convolutions [PDF]

, 2008
Debbah and Ryan have recently proved a result about the limit empirical singular distribution of the sum of two rectangular random matrices whose dimensions tend to infinity.
Benaych-Georges, Florent
core   +3 more sources

Characterizations of some free random variables by properties of conditional moments of third degree polynomials

, 2012
We investigate Laha-Lukacs properties of noncommutative random variables (processes). We prove that some families of free Meixner distributions can be characterized by the conditional moments of polynomial functions of degree 3.
Ejsmont, Wiktor
core   +1 more source

Local limit theorems in free probability theory

, 2010
In this paper, we study the superconvergence phenomenon in the free central limit theorem for identically distributed, unbounded summands. We prove not only the uniform convergence of the densities to the semicircular density but also their $L^p ...
Wang, Jiun-Chau
core   +1 more source

Limit distributions of Gaussian block ensembles

, 2015
It has been shown by Voiculescu that important classes of square independent random matrices are asymptotically free, where freeness is a noncommutative analog of classical independence. Recently, we introduced the concept of matricial freeness, which is
Lenczewski, Romuald
core   +1 more source