Shifted substitution in non-commutative multivariate power series with a view towards free probability
| dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
| dc.bibliographicCitation.volume | 2945 | |
| dc.contributor.author | Ebrahimi-Fard, Kurusch | |
| dc.contributor.author | Patras, Frédéric | |
| dc.contributor.author | Tapia, Nikolas | |
| dc.contributor.author | Zambotti, Lorenzo | |
| dc.date.accessioned | 2022-07-08T13:04:40Z | |
| dc.date.available | 2022-07-08T13:04:40Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | We study a particular group law on formal power series in non-commuting parameters induced by their interpretation as linear forms on a suitable non-commutative and non- cocommutative graded connected word Hopf algebra. This group law is left-linear and is therefore associated to a pre-Lie structure on formal power series. We study these structures and show how they can be used to recast in a group theoretic form various identities and transformations on formal power series that have been central in the context of non-commutative probability theory, in particular in Voiculescu?s theory of free probability. | eng |
| dc.description.version | publishedVersion | eng |
| dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9703 | |
| dc.identifier.uri | https://doi.org/10.34657/8741 | |
| dc.language.iso | eng | |
| dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
| dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2945 | |
| dc.relation.issn | 2198-5855 | |
| dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
| dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
| dc.subject.ddc | 510 | |
| dc.subject.other | Non-commutative probability theory | eng |
| dc.subject.other | non-commutative power series | eng |
| dc.subject.other | moments and cumulants | eng |
| dc.subject.other | combinatorial Hopf algebra | eng |
| dc.subject.other | pre-Lie algebra | eng |
| dc.title | Shifted substitution in non-commutative multivariate power series with a view towards free probability | eng |
| dc.type | Report | eng |
| dc.type | Text | eng |
| dcterms.extent | 18 S. | |
| tib.accessRights | openAccess | |
| wgl.contributor | WIAS | |
| wgl.subject | Mathematik | |
| wgl.type | Report / Forschungsbericht / Arbeitspapier |
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