Infinite divisibility and a non-commutative Boolean-to-free Bercovici–Pata bijection |
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| Authors: | ST Belinschi M Popa V Vinnikov |
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| Institution: | 1. Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada;2. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, 014700, Romania;3. Center for Advanced Studies in Mathematics at the Ben Gurion University of Negev, P.O. B. 653, Be?er Sheva 84105, Israel;4. Department of Mathematics, Ben Gurion University of Negev, Be?er Sheva 84105, Israel |
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| 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. |
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