A Noncommutative de Finetti Theorem: Invariance under Quantum Permutations is Equivalent to Freeness with Amalgamation

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A Noncommutative de Finetti Theorem: Invariance under Quantum Permutations is Equivalent to Freeness with Amalgamation. / Köstler, Claus; Speicher, Roland.

Yn: Communications in Mathematical Physics, Cyfrol 291, 31.12.2009, t. 473-490.

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Harvard

Köstler, C & Speicher, R 2009, 'A Noncommutative de Finetti Theorem: Invariance under Quantum Permutations is Equivalent to Freeness with Amalgamation', Communications in Mathematical Physics, cyfrol. 291, tt. 473-490.

APA

Köstler, C., & Speicher, R. (2009). A Noncommutative de Finetti Theorem: Invariance under Quantum Permutations is Equivalent to Freeness with Amalgamation. Communications in Mathematical Physics, 291, 473-490.

Vancouver

Köstler C, Speicher R. A Noncommutative de Finetti Theorem: Invariance under Quantum Permutations is Equivalent to Freeness with Amalgamation. Communications in Mathematical Physics. 2009 Dec 31;291:473-490.

Author

Köstler, Claus ; Speicher, Roland. / A Noncommutative de Finetti Theorem: Invariance under Quantum Permutations is Equivalent to Freeness with Amalgamation. Yn: Communications in Mathematical Physics. 2009 ; Cyfrol 291. tt. 473-490.

Bibtex - Download

@article{863ed636ed814a71bda4d5148841f97b,
title = "A Noncommutative de Finetti Theorem: Invariance under Quantum Permutations is Equivalent to Freeness with Amalgamation",
abstract = "We showthat 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 (xi )i?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.",
author = "Claus K{\"o}stler and Roland Speicher",
year = "2009",
month = dec,
day = "31",
language = "English",
volume = "291",
pages = "473--490",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer Nature",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - A Noncommutative de Finetti Theorem: Invariance under Quantum Permutations is Equivalent to Freeness with Amalgamation

AU - Köstler, Claus

AU - Speicher, Roland

PY - 2009/12/31

Y1 - 2009/12/31

N2 - We showthat 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 (xi )i?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.

AB - We showthat 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 (xi )i?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.

UR - http://hdl.handle.net/2160/8556

M3 - Article

VL - 291

SP - 473

EP - 490

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -

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