Abstract.
We study noncommutative probability spaces endowed with infinite sequences of states. Following ideas of Cabanal-Duvillard we extend the notion of conditional freeness. Free product of such spaces is justified by constructing an appropriate ⋆-representation. Finally, we provide limit theorems and describe the sequences of orthogonal polynomials related to the limit measures.
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Received: 4 November 1998 / Revised version: 22 April 1999
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Młtkowski, W. Free probability on algebras with infinitely many states. Probab Theory Relat Fields 115, 579–596 (1999). https://doi.org/10.1007/s004400050250
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DOI: https://doi.org/10.1007/s004400050250
- Mathematics Subject Classification (1991): 60B99, 46L50, 05A18