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Convolution and limit
theorems for conditionally free random variables
Marek Bożejko, Michael Leinert and Roland Speicher |
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Vol. 175 (1996), No. 2, 357–388
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Abstract |
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We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the lattice of non-crossing partitions, and from an analytic point of view, by presenting the basic formula for its R-transform. We calculate explicitly the distributions of the conditionally free Gaussian and conditionally free Poisson distribution. |
Mathematical Subject Classification 2000
Secondary: 46N50, 81S25, 46K99
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Milestones
Received: 21 October 1994
Published: 1 October 1996
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Authors |
| Marek Bożejko | |
| Mathematical Institute Uniwersytet Wrocławski Plac Grunwaldzki 2/4 50-384 Poland |
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| http://www.math.uni.wroc.pl/~bozejko/ | |
| Michael Leinert | |
| Institut für Angewandte
Mathematik Universität Heidelberg Im Neuenheimer Feld 294 D-69120 Heidelberg Germany |
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| http://www.math.uni-heidelberg.de/am/leinert.html | |
| Roland Speicher | |
| Fachrichtung Mathematik Universität des Saarlandes Postfach 151150 D-66041 Saarbrücken Germany |
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| http://www.math.uni-sb.de/ag/speicher/speicher.html | |
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