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arXiv · 1002.4390

A characterization of freeness by invariance under quantum spreading

Stephen Curran
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Abstract

We construct spaces of quantum increasing sequences, which give quantum families of maps in the sense of Soltan. We then introduce a notion of quantum spreadability for a sequence of noncommutative random variables, by requiring their joint distribution to be invariant under taking quantum subsequences. Our main result is a free analogue of a theorem of Ryll-Nardzewski: for an infinite sequence of noncommutative random variables, quantum spreadability is equivalent to free independence and identical distribution with respect to a conditional expectation.

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Stephen Curran. 2010-10-14. A characterization of freeness by invariance under quantum spreading. https://arxiv.org/abs/1002.4390

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