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

Published 1 Jul 2010 in math.OA and math.PR | (1007.0058v3)

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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