The Experts below are selected from a list of 22953 Experts worldwide ranked by ideXlab platform
Roland Speicher - One of the best experts on this subject based on the ideXlab platform.
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a noncommutative de finetti theorem invariance under quantum Permutations is equivalent to freeness with amalgamation
Communications in Mathematical Physics, 2009Co-Authors: Claus Kostler, Roland SpeicherAbstract:We show that the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen “exchangeability” (i.e., invariance of the joint distribution of the random variables under the action of the Permutation Group) to invariance under the action of the quantum Permutation Group. More precisely, for an infinite sequence of noncommutative random variables \({(x_i)_{i\in\mathbb{N}}}\) , we prove that invariance of the joint distribution of the xi’s under quantum Permutations is equivalent to the fact that the xi’s are identically distributed and free with respect to the conditional expectation onto the tail algebra of the xi’s.
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a noncommutative de finetti theorem invariance under quantum Permutations is equivalent to freeness with amalgamation
arXiv: Operator Algebras, 2008Co-Authors: Claus Kostler, Roland SpeicherAbstract:We show that the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen `exchangeability' (i.e., invariance of the joint distribution of the random variables under the action of the Permutation Group) to invariance under the action of the quantum Permutation Group. More precisely, for an infinite sequence of noncommutative random variables, we prove that invariance of their joint distribution under quantum Permutations is equivalent to the fact that the random variables are identically distributed and free with respect to the conditional expectation onto their tail algebra.
Claus Kostler - One of the best experts on this subject based on the ideXlab platform.
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a noncommutative de finetti theorem invariance under quantum Permutations is equivalent to freeness with amalgamation
Communications in Mathematical Physics, 2009Co-Authors: Claus Kostler, Roland SpeicherAbstract:We show that the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen “exchangeability” (i.e., invariance of the joint distribution of the random variables under the action of the Permutation Group) to invariance under the action of the quantum Permutation Group. More precisely, for an infinite sequence of noncommutative random variables \({(x_i)_{i\in\mathbb{N}}}\) , we prove that invariance of the joint distribution of the xi’s under quantum Permutations is equivalent to the fact that the xi’s are identically distributed and free with respect to the conditional expectation onto the tail algebra of the xi’s.
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a noncommutative de finetti theorem invariance under quantum Permutations is equivalent to freeness with amalgamation
arXiv: Operator Algebras, 2008Co-Authors: Claus Kostler, Roland SpeicherAbstract:We show that the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen `exchangeability' (i.e., invariance of the joint distribution of the random variables under the action of the Permutation Group) to invariance under the action of the quantum Permutation Group. More precisely, for an infinite sequence of noncommutative random variables, we prove that invariance of their joint distribution under quantum Permutations is equivalent to the fact that the random variables are identically distributed and free with respect to the conditional expectation onto their tail algebra.
Wojciech Mlotkowski - One of the best experts on this subject based on the ideXlab platform.
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positive definite functions on coxeter Groups with applications to operator spaces and noncommutative probability
Communications in Mathematical Physics, 2018Co-Authors: Marek Bozejko, światoslaw R Gal, Wojciech MlotkowskiAbstract:A new class of positive definite functions related to colour-length function on arbitrary Coxeter Group is introduced. Extensions of positive definite functions, called the Riesz–Coxeter product, from the Riesz product on the Rademacher (Abelian Coxeter) Group to arbitrary Coxeter Group is obtained. Applications to harmonic analysis, operator spaces and noncommutative probability are presented. Characterization of radial and colour-radial functions on dihedral Groups and infinite Permutation Group are shown.
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positive definite functions on coxeter Groups with applications to operator spaces and noncommutative probability
arXiv: Operator Algebras, 2017Co-Authors: Marek Bozejko, światoslaw R Gal, Wojciech MlotkowskiAbstract:A new class of positive definite functions related to colour-length function on arbitrary Coxeter Group is introduced. Extensions of positive definite functions, called the Riesz-Coxeter product, from the Riesz product on the Rademacher (Abelian Coxeter) Group to arbitrary Coxeter Group is obtained. Applications to harmonic analysis, operator spaces and noncommutative probability is presented. Characterization of radial and colour-radial functions on dihedral Groups and infinite Permutation Group are shown.
Marek Bozejko - One of the best experts on this subject based on the ideXlab platform.
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positive definite functions on coxeter Groups with applications to operator spaces and noncommutative probability
Communications in Mathematical Physics, 2018Co-Authors: Marek Bozejko, światoslaw R Gal, Wojciech MlotkowskiAbstract:A new class of positive definite functions related to colour-length function on arbitrary Coxeter Group is introduced. Extensions of positive definite functions, called the Riesz–Coxeter product, from the Riesz product on the Rademacher (Abelian Coxeter) Group to arbitrary Coxeter Group is obtained. Applications to harmonic analysis, operator spaces and noncommutative probability are presented. Characterization of radial and colour-radial functions on dihedral Groups and infinite Permutation Group are shown.
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positive definite functions on coxeter Groups with applications to operator spaces and noncommutative probability
arXiv: Operator Algebras, 2017Co-Authors: Marek Bozejko, światoslaw R Gal, Wojciech MlotkowskiAbstract:A new class of positive definite functions related to colour-length function on arbitrary Coxeter Group is introduced. Extensions of positive definite functions, called the Riesz-Coxeter product, from the Riesz product on the Rademacher (Abelian Coxeter) Group to arbitrary Coxeter Group is obtained. Applications to harmonic analysis, operator spaces and noncommutative probability is presented. Characterization of radial and colour-radial functions on dihedral Groups and infinite Permutation Group are shown.
Derek F. Holt - One of the best experts on this subject based on the ideXlab platform.
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computing conjugacy class representatives in Permutation Groups
Journal of Algebra, 2006Co-Authors: John Cannon, Derek F. HoltAbstract:Abstract We describe a significantly improved algorithm for computing the conjugacy classes of a finite Permutation Group with trivial soluble radical. We rely on existing methods for Groups that are almost simple, and we are concerned here only with the reduction of the general case to the almost simple case.
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automorphism Group computation and isomorphism testing in finite Groups
Journal of Symbolic Computation, 2003Co-Authors: John Cannon, Derek F. HoltAbstract:A new method for computing the automorphism Group of a finite Permutation Group and for testing two such Groups for isomorphism is described. Some performance statistics are included for an implementation of these algorithms in the Magma language.
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Representing the Quotient Groups of a Finite Permutation Group
Journal of Algebra, 2002Co-Authors: Derek F. Holt, Jacqueline WaltonAbstract:Abstract Let G be a Permutation Group of finite degree d. We prove that the product of the orders of the composition factors of G that are not alternating Groups acting naturally, in a sense that will be made precise, is bounded by cd − 1/d, where c = 4.5. We use this to prove that any quotient G/N of G has a faithful Permutation representation of degree at most cd − 1.
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computing the subGroups of a Permutation Group
Journal of Symbolic Computation, 2001Co-Authors: John Cannon, Bruce C Cox, Derek F. HoltAbstract:A new method for computing the conjugacy classes of subGroups of a finite Group is described.