Non-commutative functions and the non-commutative free Lévy-Hinčin formula

Mihai Popa; Victor Vinnikov

doi:10.1016/j.aim.2012.12.013

Non-commutative functions and the non-commutative free Lévy-Hinčin formula

Mihai Popa
, Victor Vinnikov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

The paper is discussing infinite divisibility in the setting of operator-valued boolean, free and, more general, c-free independences. Particularly, using Hilbert bimodule and non-commutative function techniques, we obtain analogues of the Lévy-Hinčin integral representation for infinitely divisible real measures.

Original language	English
Pages (from-to)	131-157
Number of pages	27
Journal	Advances in Mathematics
Volume	236
DOIs	https://doi.org/10.1016/j.aim.2012.12.013
State	Published - 1 Mar 2013

Keywords

Free probability
Fully matricial functions
Infinite divisibility
Non-commutative functions
R-transform

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2012.12.013

Cite this

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title = "Non-commutative functions and the non-commutative free L{\'e}vy-Hin{\v c}in formula",

abstract = "The paper is discussing infinite divisibility in the setting of operator-valued boolean, free and, more general, c-free independences. Particularly, using Hilbert bimodule and non-commutative function techniques, we obtain analogues of the L{\'e}vy-Hin{\v c}in integral representation for infinitely divisible real measures.",

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AU - Vinnikov, Victor

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N2 - The paper is discussing infinite divisibility in the setting of operator-valued boolean, free and, more general, c-free independences. Particularly, using Hilbert bimodule and non-commutative function techniques, we obtain analogues of the Lévy-Hinčin integral representation for infinitely divisible real measures.

AB - The paper is discussing infinite divisibility in the setting of operator-valued boolean, free and, more general, c-free independences. Particularly, using Hilbert bimodule and non-commutative function techniques, we obtain analogues of the Lévy-Hinčin integral representation for infinitely divisible real measures.

KW - Free probability

KW - Fully matricial functions

KW - Infinite divisibility

KW - Non-commutative functions

KW - R-transform

UR - https://www.scopus.com/pages/publications/84873247266

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DO - 10.1016/j.aim.2012.12.013

M3 - Article

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SN - 0001-8708

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EP - 157

JO - Advances in Mathematics

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ER -

Non-commutative functions and the non-commutative free Lévy-Hinčin formula

Abstract

Keywords

ASJC Scopus subject areas

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