Infinite divisibility and a non-commutative Boolean-to-free Bercovici-Pata bijection

S. T. Belinschi, M. Popa, V. Vinnikov

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue for the Bercovici-Pata bijection. An important tool is Voiculescu's subordination property for operator-valued free convolution.

Original languageEnglish
Pages (from-to)94-123
Number of pages30
JournalJournal of Functional Analysis
Volume262
Issue number1
DOIs
StatePublished - 1 Jan 2012

Keywords

  • Bercovici-Pata bijection
  • Limit theorems
  • Non-commutative functions
  • Operator-valued free probability

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