T. Banica, S. Curran, и R. Speicher. (2009)cite arxiv:0907.3314Comment: Published in at http://dx.doi.org/10.1214/10-AOP619 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org).
DOI: 10.1214/10-AOP619
Аннотация
We study sequences of noncommutative random variables which are invariant
under "quantum transformations" coming from an orthogonal quantum group
satisfying the "easiness" condition axiomatized in our previous paper. For 10
easy quantum groups, we obtain de Finetti type theorems characterizing the
joint distribution of any infinite quantum invariant sequence. In particular,
we give a new and unified proof of the classical results of de Finetti and
Freedman for the easy groups S_n, O_n, which is based on the combinatorial
theory of cumulants. We also recover the free de Finetti theorem of Köstler
and Speicher, and the characterization of operator-valued free semicircular
families due to Curran. We consider also finite sequences, and prove an
approximation result in the spirit of Diaconis and Freedman.
Описание
[0907.3314] De Finetti theorems for easy quantum groups
cite arxiv:0907.3314Comment: Published in at http://dx.doi.org/10.1214/10-AOP619 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
%0 Journal Article
%1 banica2009finetti
%A Banica, Teodor
%A Curran, Stephen
%A Speicher, Roland
%D 2009
%K probability theory
%R 10.1214/10-AOP619
%T De Finetti theorems for easy quantum groups
%U http://arxiv.org/abs/0907.3314
%X We study sequences of noncommutative random variables which are invariant
under "quantum transformations" coming from an orthogonal quantum group
satisfying the "easiness" condition axiomatized in our previous paper. For 10
easy quantum groups, we obtain de Finetti type theorems characterizing the
joint distribution of any infinite quantum invariant sequence. In particular,
we give a new and unified proof of the classical results of de Finetti and
Freedman for the easy groups S_n, O_n, which is based on the combinatorial
theory of cumulants. We also recover the free de Finetti theorem of Köstler
and Speicher, and the characterization of operator-valued free semicircular
families due to Curran. We consider also finite sequences, and prove an
approximation result in the spirit of Diaconis and Freedman.
@article{banica2009finetti,
abstract = {We study sequences of noncommutative random variables which are invariant
under "quantum transformations" coming from an orthogonal quantum group
satisfying the "easiness" condition axiomatized in our previous paper. For 10
easy quantum groups, we obtain de Finetti type theorems characterizing the
joint distribution of any infinite quantum invariant sequence. In particular,
we give a new and unified proof of the classical results of de Finetti and
Freedman for the easy groups S_n, O_n, which is based on the combinatorial
theory of cumulants. We also recover the free de Finetti theorem of K\"ostler
and Speicher, and the characterization of operator-valued free semicircular
families due to Curran. We consider also finite sequences, and prove an
approximation result in the spirit of Diaconis and Freedman.},
added-at = {2020-02-06T15:17:03.000+0100},
author = {Banica, Teodor and Curran, Stephen and Speicher, Roland},
biburl = {https://www.bibsonomy.org/bibtex/2b2a42a2bc0d06e4260b531c61dee1560/kirk86},
description = {[0907.3314] De Finetti theorems for easy quantum groups},
doi = {10.1214/10-AOP619},
interhash = {245c5a90004b58643046c65199aa0e97},
intrahash = {b2a42a2bc0d06e4260b531c61dee1560},
keywords = {probability theory},
note = {cite arxiv:0907.3314Comment: Published in at http://dx.doi.org/10.1214/10-AOP619 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)},
timestamp = {2020-02-06T15:17:12.000+0100},
title = {De Finetti theorems for easy quantum groups},
url = {http://arxiv.org/abs/0907.3314},
year = 2009
}