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Demonstratio Mathematica, ISSN 0420-1213, 06/2012, Volume 45, Issue 2, pp. 399 - 413
The main purpose of this paper is to extend our previous construction of -Fock spaces from a given Yang–Baxter operator satisfying the inequalities −1 ≤ ≤ 1 to... 
60H04 | 05C30 | 46L54
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 12/2019, Volume 100, Issue 3, pp. 987 - 1012
We present a combinatorial approach to the infinitesimal distribution of the Gaussian orthogonal ensemble (goe). In particular, we show how the infinitesimal... 
15B52 | 05D40 | 46L54 (primary) | 60B20 (secondary)
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 06/2018, Volume 59, Issue 6, p. 63511
We study an extension of Bernstein theorem to the setting of quantum groups. For a d-tuple of free identically distributed random variables, we consider a... 
INVARIANCE | ALGEBRAS | FREENESS | FAMILIES | PRODUCT | PHYSICS, MATHEMATICAL | HOPF IMAGES
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 12/2014, Volume 332, Issue 3, pp. 955 - 980
We consider a notion of bi-freeness for systems of non-commutative random variables with two faces, one of left variables and another of right variables. This... 
Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | COMMUTING RANDOM-VARIABLES | CUMULANTS | ALGEBRAS | MULTIPLICATION | PHYSICS, MATHEMATICAL | Algebra
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 09/2019, Volume 119, Issue 3, pp. 814 - 840
Commutative shuffle products are known to be intimately related to universal formulas for products, exponentials and logarithms in group theory as well as in... 
16T05 | 16T30 (secondary) | 16T10 | 46L53 | 46L54 (primary) | HOPF-ALGEBRAS | SERIES | THEOREM | DISTRIBUTIONS | MATHEMATICS | TREES | MONOTONE | CUMULANTS | IDEMPOTENTS | BIALGEBRAS | Mathematics | Rings and Algebras
Journal Article
Inventiones mathematicae, ISSN 1432-1297, 2012, Volume 190, Issue 3, pp. 647 - 697
Given two positive integers n and k and a parameter t∈(0,1), we choose at random a vector subspace V n ⊂ℂ k ⊗ℂ n of dimension N∼tnk. We show that the set of... 
15A52 | Mathematics, general | Mathematics | 52A22 | 46L54 | MATHEMATICS | FREE CONVOLUTION | REGULARITY | RANDOM-VARIABLES | ENTROPY
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 10/2017, Volume 273, Issue 7, pp. 2488 - 2520
Let X1,X2,…,Xn denote i.i.d. centered standard normal random variables, then the law of the sample variance Qn=∑i=1n(Xi−X‾)2 is the χ2-distribution with n−1... 
Sample variance | Cancellation of free cumulants | Free infinite divisibility | Wigner semicircle law | MATHEMATICS | CUMULANTS
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 11/2019, Volume 218, Issue 2, pp. 341 - 411
Since the 1970’s, physicists and mathematicians who study random matrices in the GUE or GOE models are aware of intriguing connections between integrals of... 
Mathematics, general | Mathematics | MATHEMATICS | EQUATIONS | MODULI SPACE | LIMIT | UNITARY | DIMENSION | Physicists | Analysis | Enumeration | Integrals | Mapping | Commutators | Asymptotic methods | Matrix methods | Subgroups
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 6/2019, Volume 32, Issue 2, pp. 1051 - 1075
We consider the spherical integral of real symmetric or Hermitian matrices when the rank of one matrix is one. We prove the existence of the full asymptotic... 
15B52 | Random matrices | Free probability | Asymptotic expansion | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Spherical integral | 46L54 | STATISTICS & PROBABILITY
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2017, Volume 2017, Issue 18, pp. 5710 - 5750
Easy quantum groups form a class of compact matrix quantum groups which are completely determined by set partitions. They have been defined in 2009 by Banica... 
MATHEMATICS | FUSION RULES | FREE WREATH PRODUCT | Operator Algebras | Quantum Algebra | Mathematics
Journal Article
Probability theory and related fields, ISSN 1432-2064, 2012, Volume 157, Issue 3-4, pp. 777 - 815
Journal Article
Journal of theoretical probability, ISSN 1572-9230, 2018, Volume 33, Issue 1, pp. 268 - 294
We study the distribution (with respect to the vacuum state) of a family of partial sums Sm of position operators on weakly monotone Fock space. We show that... 
Monotone independence and convolution | Semicircle law | Generalized Catalan recurrences | Non-commutative probability | INDEPENDENCE | 60B99 | STATISTICS & PROBABILITY | 46L53 | 05A18 | 46L54
Journal Article
Science China Mathematics, ISSN 1674-7283, 5/2019, Volume 62, Issue 5, pp. 921 - 934
Inspired by Speicher's multidimensional free central limit theorem and semicircle families, we prove an infinite dimensional compound Poisson limit theorem in... 
multidimensional free Poisson distributions | Mathematics | multidimensional free infinitely divisible distributions | Applications of Mathematics | free probability | 46L54 | MATHEMATICS | MATHEMATICS, APPLIED | FREE PRODUCT
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 9/2013, Volume 26, Issue 3, pp. 855 - 869
We study the partial transposition W Γ=(id⊗t)W∈M dn (ℂ) of a Wishart matrix W∈M dn (ℂ) of parameters (dn,dm). Our main result is that, with d→∞, the law of mW... 
81P45 | Partial transposition | Wishart matrix | Probability Theory and Stochastic Processes | 60B20 | Mathematics | Statistics, general | Free Poisson law | 46L54 | STATISTICS & PROBABILITY | Probability | Operator Algebras | Quantum Physics | Physics
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 05/2010, Volume 153, Issue 1, pp. 23 - 54
We obtain new Bass-Serre-type rigidity results for III equivalence relations and their von Neumann algebras, coining from free ergodic actions of free products... 
MATHEMATICS | REPRESENTATIONS | AMALGAMATED FREE-PRODUCTS | TENSOR-PRODUCTS | MALLEABLE ACTIONS | II1 FACTORS | EQUIVALENCE | Mathematics - Operator Algebras | 46L55 | 46L10 | 46L54
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 10/2019, Volume 13, Issue 7, pp. 3023 - 3089
In this paper, the notion of bi-Boolean independence for non-unital pairs of algebras is introduced thereby extending the notion of Boolean independence to... 
Operator Theory | Bi-Boolean independence | Analysis | Mathematics, general | B- $$(\ell , r)$$ ( ℓ , r ) -cumulants | Mathematics | Primary 46L53 | Bi-Boolean partial transforms | Secondary 46L54 | B-$$(\ell , r)$$(ℓ,r)-cumulants | Algebra
Journal Article
Jahresbericht der Deutschen Mathematiker-Vereinigung, ISSN 0012-0456, 3/2017, Volume 119, Issue 1, pp. 3 - 30
This article is an invitation to the world of free probability theory. This theory was introduced by Dan Voiculescu at the beginning of the 1980’s and has... 
Random matrix | Non-commutative distribution | Asymptotic representation theory | Mathematics, general | Mathematics | Free probability theory | 46L54
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 9/2019, Volume 32, Issue 3, pp. 1220 - 1251
We provide a perturbative expansion for the empirical spectral distribution of a Hermitian matrix with large size perturbed by a random matrix with small... 
Perturbation theory | Band matrices | 47A55 | Probability Theory and Stochastic Processes | 60B20 | Mathematics | Statistics, general | Wigner matrices | Hilbert transform | 15A52 | Random matrices | Spectral density | 46L54 | BROWNIAN-MOTION | STATISTICS & PROBABILITY | Probability
Journal Article
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