Results 11 to 20 of about 490 (43)
A survey on the effects of free and boolean convolutions on Cauchy-Stieltjes Kernel families
Probability Surveys, 2022 In the setting of noncommutative probability theory and in analogy with the theory of natural exponential families (NEFs), a theory of Cauchy-Stieltjes Kernel (CSK) families has been recently introduced. It is based on the Cauchy-Stieltjes kernel (1 − θx)
Raouf Fakhfakh
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EXACTNESS OF CUNTZ–PIMSNER C*-ALGEBRAS [PDF]
Proceedings of the Edinburgh Mathematical Society, 1999 Let $H$ be a full Hilbert bimodule over a $C^*$-algebra $A$. We show that the Cuntz–Pimsner algebra associated to $H$ is exact if and only if $A$ is exact.
K. Dykema, D. Shlyakhtenko
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Itô's formula for noncommutative $C^2$ functions of free Itô processes
Documenta Mathematica, 2022 In a recent paper, the author introduced a rich class NC(R) of “noncommutative C” functions R → C whose operator functional calculus is k-times differentiable and has derivatives expressible in terms of multiple operator integrals (MOIs).
Evangelos A. Nikitopoulos
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CONVERGENCE OF THE FOURTH MOMENT AND INFINITE DIVISIBILITY [PDF]
, 2013 In this note we prove that, for infinitely divisible laws, con- vergence of the fourth moment to 3 is sufficient to ensure convergence in law to the Gaussian distribution. Our results include infinitely divisible measures with respect to classical, free,
Octavio Arizmendi
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The Operator Hilbert Space OH and Type III Von Neumann Algebras [PDF]
, 2002 A proof is given to show that the operator Hilbert space OH does not embed completely isomorphically into the predual of a semi‐finite von Neumann algebra. This complements Junge's recent result, which admits such an embedding in the non‐semi‐finite case.
G. Pisier
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Topological orbit dimension of MF C*-algebras and NFD algebras
, 2020 This paper is a continuation of our work on D. Voiculescu’s topological free entropy dimension δtop (x1, . . . ,xn) for a family {x1, . . . ,xn} of elements in a unital C*-algebra.
Qihui Li +3 more
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Fuss-Catalan numbers in noncommutative probability
Documenta Mathematica, 2010 We prove that if p, r ∈ R, p ≥ 1 and 0 ≤ r ≤ p then the Fuss-Catalan sequence ( mp+r m ) r mp+r is positive definite. We study the family of the corresponding probability measures μ(p, r) on R from the point of view of noncommutative probability.
W. Mlotkowski
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The one dimensional free Poincaré inequality [PDF]
, 2011 In this paper we discuss the natural candidate for the one dimensional free Poincare inequality. Two main strong points sustain this candidacy. One is the random matrix heuristic and the other the relations with the other free functional inequalities ...
M. Ledoux, Ionel Popescu
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Non-commutative independence of algebras and applications to probability
, 2010 We present the notions of independence, which appear in non-commutative probability. The basic ones are free, boolean and monotonic independences, formulated for families of algebras indexed by totally ordered set.
J. Wysoczánski
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Central Limit Theorems for the Brownian motion on large unitary groups [PDF]
, 2009 In this paper, we are concerned with the large N limit of linear combinations of the entries of a Brownian motion on the group of N by N unitary matrices. We prove that the process of such a linear combination converges to a Gaussian one.
De France +3 more
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