Infinite divisibility and a non-commutative Boolean-to-free Bercovici-Pata bijection
Operator Algebras
2011-11-24 v3 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.
Keywords
Cite
@article{arxiv.1007.0058,
title = {Infinite divisibility and a non-commutative Boolean-to-free Bercovici-Pata bijection},
author = {Serban T. Belinschi and Mihai Popa and Victor Vinnikov},
journal= {arXiv preprint arXiv:1007.0058},
year = {2011}
}
Comments
26 pages, LaTeX