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Freeness
characterizations on free chaos spaces
Solesne Bourguin and Ivan Nourdin |
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Vol. 305 (2020), No. 2, 447–472
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DOI: 10.2140/pjm.2020.305.447
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Abstract |
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We deal with characterizing the freeness and asymptotic freeness of free multiple integrals with respect to a free Brownian motion or a free Poisson process. We obtain three characterizations of freeness, in terms of contraction operators, covariance conditions, and free Malliavin gradients. We show how these characterizations can be used in order to obtain limit theorems, transfer principles, and asymptotic properties of converging sequences. |
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Keywords
free probability, Wigner integrals, free Poisson integrals,
free Malliavin calculus, characterization of freeness, free
fourth movement theorems
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Mathematical Subject Classification 2010
Primary: 46L54
Secondary: 68H07, 60H30
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Milestones
Received: 14 May 2017
Revised: 8 November 2019
Accepted: 9 November 2019
Published: 29 April 2020
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Authors |
| Solesne Bourguin | |
| Department of Mathematics and
Statistics Boston University Boston, MA United States |
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| Ivan Nourdin | |
| Department of Mathematics University of Luxembourg Esch-sur-Alzette Luxembourg |
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