147 research outputs found
On the rate of convergence and Berry-Esseen type theorems for a multivariate free central limit theorem
We address the question of a Berry Esseen type theorem for the speed of
convergence in a multivariate free central limit theorem. For this, we estimate
the difference between the operator-valued Cauchy transforms of the normalized
partial sums in an operator-valued free central limit theorem and the Cauchy
transform of the limiting operator-valued semicircular element.Comment: 14 page
Continuous Family of Invariant Subspaces for R-diagonal Operators
We show that every R-diagonal operator x has a continuous family of invariant
subspaces relative to the von Neumann algebra generated by x. This allows us to
find the Brown measure of x and to find a new conceptual proof that
Voiculescu's S-transform is multiplicative. Our considerations base on a new
concept of R-diagonality with amalgamation, for which we give several
equivalent characterizations.Comment: 35 page
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