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Probability Theory and Related Fields

, Volume 115, Issue 4, pp 579–596 | Cite as

Free probability on algebras with infinitely many states

  • Wojciech Młtkowski

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.

Mathematics Subject Classification (1991): 60B99, 46L50, 05A18 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Wojciech Młtkowski
    • 1
  1. 1.Mathematical Institute, University of Wroclstrok;, Pl. Grunwaldzki 2/4, 50-384 Wroclstrok;, Poland. e-mail: mlotkow@math.uni.wroc.plPL

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