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Abstract: We study sequences of noncommutative random variables which are invariantunder -quantum transformations- coming from an orthogonal quantum groupsatisfying the -easiness- condition axiomatized in our previous paper. For 10easy quantum groups, we obtain de Finetti type theorems characterizing thejoint distribution of any infinite quantum invariant sequence. In particular,we give a new and unified proof of the classical results of de Finetti andFreedman for the easy groups S n, O n, which is based on the combinatorialtheory of cumulants. We also recover the free de Finetti theorem of K\-ostlerand Speicher, and the characterization of operator-valued free semicircularfamilies due to Curran. We consider also finite sequences, and prove anapproximation result in the spirit of Diaconis and Freedman.



Author: Teodor Banica, Stephen Curran, Roland Speicher

Source: https://arxiv.org/







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