An example of a Boolean-free type central limit theorem

• Autorzy: Kula A. , Wysoczański J.
• Języki publikacji: EN

Abstrakty

EN

We construct a product of Hilbert spaces and associated product of operators, which generalizes the boolean and the free products and provides a model for new independence. The related Central Limit Theorem is proved.

Słowa kluczowe

EN

free independence; boolean independence; noncommutative CLT; partially ordered sets

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2013
• Tom: Vol. 33, Fasc. 2
• Strony: 341--352
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Kula A.

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

autor

Wysoczański J.

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

Bibliografia

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• [3] J. Faraut and A. Korányi, Analysis on Symmetric Cones, Oxford Math. Monogr., Oxford Sci. Publ., Clarendon Press, Oxford University Press, New York 1994.
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• [5] A. Kula and J. Wysoczański, Noncommutative Brownian motions indexed by partially ordered sets, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13 (4) (2010), pp. 629-661.
• [6] N. Muraki, Monotonic independence, monotonic central limit theorem and monotonic law of small numbers, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 4 (1) (2001), pp. 39-58.
• [7] D. Voiculescu, Symmetries of some reduced free product C∗-algebras, in: Operator Algebras and Their Connections with Topology and Ergodic Theory (Buşteni, 1983), Lecture Notes in Math., Vol. 1132, Springer, Berlin 1985, pp. 556-588.
• [8] J. Wysoczański, Monotonic independence associated with partially ordered sets, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10 (1) (2007), pp. 17-41.
• [9] J. Wysoczański, bm-central limit theorems for positive definite real symmetric matrices, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11 (1) (2008), pp. 33-51.
• [10] J. Wysoczański, bm-independence and bm-central limit theorems associated with symmetric cones, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13 (3) (2010), pp. 461-488.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).