bm-independence and central limit theorems associated with symmetric cones

• Autorzy: Janusz Wysoczański
• Języki publikacji: EN

Abstrakty

EN

We present a generalization of the classical central limit theorem to the case of non-commuting random variables which are bm-independent and indexed by a partially ordered set. As the set of indices I we consider discrete lattices in symmetric positive cones, with the order given by the cones. We show that the limit measures have moments which satisfy recurrences generalizing the recurrence for the Catalan numbers.

Kategorie tematyczne

• 46L54: Free probability and free operator algebras
• 81R50: Quantum groups and related algebraic methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 78
• Numer: 1
• Strony: 315-320

Daty

wydano

2007

Twórcy

autor

Janusz Wysoczański

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/bc78-0-24