Infinite divisibility and a non-commutative Boolean-to-free Bercovici-Pata bijection
Serban T. Belinschi, Mihai Popa, and Victor Vinnikov
TL;DR
This paper develops an operator-valued analogue of the Bercovici-Pata bijection within non-commutative probability, utilizing fully matricial functions and Voiculescu's subordination to analyze infinite divisibility and limit theorems.
Contribution
It introduces a novel operator-valued Bercovici-Pata bijection, extending classical results to the non-commutative setting using advanced functional analysis tools.
Findings
Established an operator-valued Bercovici-Pata bijection.
Applied Voiculescu's subordination to non-commutative convolution.
Provided new insights into infinite divisibility in operator-valued probability.
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 of the Bercovici-Pata bijection. An important tool is Voiculescu's subordination property for operator-valued free convolution.
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