In this paper,we construct random two-faced families of matrices with non-Gaussian entries to approximate a bi-free central limit distribution with a positive definite covariance matrix.We prove that,under modest cond...
Let p and q be two fixed non zero integers verifying the condition gcd(p,q) = 1. We check solutions in non zero integers a1,b1,a2,b2 and a3 for the following Diophantine equations: (B1) (B2) . The equations (B1) and (...
If a semicircular element and the diagonal subalgebra of a matrix algebra are free in a finite von Neumann algebra (with respect to a normal trace), then, up to the conjugation by a diagonal unitary element, all ent...
We consider a central hyperplane arrangement in a three-dimensional vector space. The definition of characteristic form to a hyperplane arrangement is given and we could make use of characteristic form to judge the re...
The notion of operator-valued free Fisher information was introduced.It is a generalization of free Fisher information which was defined by D.Voiculescu on tracial von Neumann algebras.It is proved that the operator-v...