dc.creator |
Février, Maxime |
|
dc.creator |
Mastnak, Mitja |
|
dc.creator |
Nica, Alexandru |
|
dc.creator |
Szpojankowski, Kamil |
|
dc.date.accessioned |
2024-09-18T16:11:29Z |
|
dc.date.available |
2024-09-18T16:11:29Z |
|
dc.date.issued |
2015-08-2 |
|
dc.identifier.issn |
0196-8858 |
|
dc.identifier.uri |
https://dx.doi.org/10.1016/j.aam.2019.06.002 |
|
dc.identifier.uri |
http://library2.smu.ca/xmlui/handle/01/32033 |
|
dc.description |
Published version |
en_CA |
dc.description.abstract |
We consider two extensions of free probability that have been studied in the research literature, and are based on the notions of <i>c-freeness</i> and respectively of <i>infinitesimal freeness</i> for noncommutative random variables. In a 2012 paper, Belinschi and Shlyakhtenko pointed out a connection between these two frameworks, at the level of their operations of 1-dimensional free additive convolution. Motivated by that, we propose a construction which produces a multi-variate version of the Belinschi-Shlyakhtenko result, together with a result concerning free products of multi-variate noncommutative distributions. Our arguments are based on the combinatorics of the specific types of cumulants used in c-free and in infinitesimal free probability. They work in a rather general setting, where the initial data consists of a vector space V given together with a linear map Δ : V → V ⊗ V. In this setting, all the needed brands of cumulants live in the guise of families of multilinear functionals on V, and our main result concerns a certain transformation Δ<sup>*</sup> on such families of multilinear functionals. |
en_CA |
dc.description.provenance |
Submitted by Anna Labrador (anna.labrador@smu.ca) on 2024-09-18T16:11:29Z
No. of bitstreams: 1
Mastnak_Mitja_2015.pdf: 794687 bytes, checksum: 7c077bdb7d985bb35a2e9f5aed9c1ba2 (MD5) |
en |
dc.description.provenance |
Made available in DSpace on 2024-09-18T16:11:29Z (GMT). No. of bitstreams: 1
Mastnak_Mitja_2015.pdf: 794687 bytes, checksum: 7c077bdb7d985bb35a2e9f5aed9c1ba2 (MD5)
Previous issue date: 2019-09 |
en |
dc.language.iso |
en |
en_CA |
dc.publisher |
Elsevier Inc |
en_CA |
dc.relation.uri |
https://doi.org/10.1016/j.aam.2019.06.002 |
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dc.rights |
© 2019 Elsevier Inc. All rights reserved. |
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dc.subject.lcsh |
Free probability theory |
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dc.subject.lcsh |
Random variables |
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dc.title |
A construction which relates c-freeness to infinitesimal freeness |
en_CA |
dc.type |
Text |
en_CA |
dcterms.bibliographicCitation |
Advances in applied mathematics 110, 299-341. (2015) |
en_CA |