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A characterization of freeness by invariance under quantum spreading
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Stephen Curran
Published/Copyright:
April 14, 2011
Abstract
We construct spaces of quantum increasing sequences, which give quantum families of maps in the sense of Sołtan. 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.
Received: 2010-02-23
Revised: 2010-06-08
Published Online: 2011-04-14
Published in Print: 2011-October
© Walter de Gruyter Berlin · New York 2011
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- Ranks of invariant subspaces of the Hardy space over the bidisk
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Articles in the same Issue
- Period and index in the Brauer group of an arithmetic surface
- A characterization of freeness by invariance under quantum spreading
- Canonical bases and KLR-algebras
- Ranks of invariant subspaces of the Hardy space over the bidisk
- The Kähler–Ricci flow on Hirzebruch surfaces
- A correction to Hasse's version of the Grunwald–Hasse–Wang theorem
- On the regularized Siegel–Weil formula (the second term identity) and non-vanishing of theta lifts from orthogonal groups
