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- W1569352001 abstract "We introduce a family of quantum semigroups and their natural coactions on noncommutative polynomials. We present three invariance conditions, associated with these coactions, for the joint distribution of sequences of selfadjoint noncommutative random variables. For one of the invariance conditions, we prove that the joint distribution of an infinite sequence of noncommutative random variables satisfies it is equivalent to the fact that the sequence of the random variables are identically distributed and boolean independent with respect to the conditional expectation onto its tail algebra. This is a boolean analogue of de Finetti theorem on exchangeable sequences. In the end of the paper, we will discuss the other two invariance conditions which lead to some trivial results." @default.
- W1569352001 created "2016-06-24" @default.
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- W1569352001 date "2014-03-07" @default.
- W1569352001 modified "2023-09-24" @default.
- W1569352001 title "A noncommutative De Finetti theorem for boolean independence" @default.
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- W1569352001 doi "https://doi.org/10.48550/arxiv.1403.1772" @default.
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