DE FINETTI THEOREMS FOR EASY QUANTUM GROUPS

• 成果类型: Article
• 署名作者: Banica, Teodor; Curran, Stephen; Speicher, Roland
• 署名单位: CY Cergy Paris Universite; University of California System; University of California Los Angeles; Queens University - Canada; Saarland University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP619
• 发表日期: 2012
• 页码: 401-435
• 关键词: integration; INVARIANTS; limit

摘要

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 Kostler 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.