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Rectangular random matrices, related convolution
We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates. It appears...
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A limit theorem for products of free unitary operators
This paper establishes necessary and sufficient conditions for the sequence of products of freely independent unitary operators to converge in...
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The Lebesgue decomposition of the free additive convolution of two probability distributions
We prove that the free additive convolution of two Borel probability measures supported on the real line can have a component that is singular...
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Infinitely divisible distributions for rectangular free convolution: classification and matricial interpretation
In a previous paper (Benaych-Georges in Related Convolution 2006), we defined the rectangular free convolution ⊞ λ . Here, we investigate the related...
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Remarks on the r and Δ convolutions
In this paper we study the properties of the r –deformation introduced in [B1]. We observe that the associated convolution coming from the...
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Cumulants for random matrices as convolutions on the symmetric group
In this paper, we show that free cumulants can be naturally seen as the limiting value of ``cumulants of matrices''. We define these objects as...
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Failure of the Raikov Theorem for Free Random Variables
We show that the sum of two free random variables can have a free Poisson law without any of them having a free Poisson law.
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Free fisher information and amalgamated freeness
The notion of operator-valued free Fisher information was introduced. It is a generalization of free Fisher information which was defined by D....
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Multivariable moment problems
In this paper we solve moment problems for Poisson transforms and, more generally, for completely positive linear maps on unital C * -algebras...
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The Lévy-Itô decomposition in free probability
In this paper we prove the free analog of the Lévy-Itô decomposition for Lévy processes. A significant part of the proof consists of introducing free...
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Atoms and regularity for measures in a partially defined free convolution semigroup
Consider a Borel probability measure μ on the real line, and denote by { μ t : t ≥1} the free additive convolution semigroup defined by Nica and...
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Non injectivity of the q-deformed von Neumann algebra
In this paper we prove that the von Neumann algebra generated by q-gaussians is not injective as soon as the dimension of the underlying Hilbert...
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Free transportation cost inequalities via random matrix approximation
By means of random matrix approximation procedure, we re-prove Biane and Voiculescu’s free analog of Talagrand’s transportation cost inequality for...
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Irreducible Subfactors Derived from Popa’s Construction for Non-Tracial States
For an inclusion of the form \(\mathbb{C} \subseteq M_n (\mathbb{C})\)...
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The Atoms of the Free Multiplicative Convolution of Two Probability Distributions
We determine the atoms of the free multiplicative convolution of two measures supported on the unit circle or on the positive real line. Analogous...
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Logarithmic Sobolev Inequalities, Matrix Models and Free Entropy
We give two applications of logarithmic Sobolev inequalities to matrix models and free probability. We also provide a new characterization of...