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2016 | 14 (20) | 65-74

Article title

Podstawowe pojęcia wolnej probabilistyki

Authors

Content

Title variants

EN
Basic concepts of free probability theory

Languages of publication

PL EN

Abstracts

Free probability theory was created by Dan Voiculescu, motivated by his efforts to understand special classes of von Neumann algebras. In the following we will give, mostly from the probability point of view, a survey on some of the basic ideas and results of free probability theory and show that in free probability theory, the role of Wigner’s semicircle distribution is analogous to that of the normal distribution in classical probability theory.

Year

Issue

Pages

65-74

Physical description

Contributors

References

  • Accardi L., Bożejko M., 1998, Interacting Fock spaces and gaussianization of probability measures, Infinite Dimensional Analysis Quantum Probability and Related Topics, no. 1 (4), s. 663–670.
  • Avitzour D., 1982, Free products of C*-algebras, Transactions of American Mathematical Society, vol. 271, s. 423–465.
  • Bożejko M., 1975, Sets with minimal constant in discrete noncommutative groups, Proceedings American Mathematical Society, vol. 51, s. 407–412.
  • Bożejko M.,, 1986, Positive definite functions on the free group and the noncommutative Riesz product, Bollettino dell’Unione Matematica Italiana A, no. (6) 4, s. 13–21.
  • Bożejko M., Bryc W., 2006, On a class of free Lévy laws related to a regression problem, Journal of Functional Analysis, vol. 236, s. 59–77.
  • Bożejko M., Leinert M., Speicher R., 1996, Convolution and limit theorems for conditionally free random variables, Pacific Journal of Mathematics, vol. 175 no. 2, s. 357–388.
  • Chihara T.S., 1978, An Introduction to Orthogonal Polynomials, Mathematics and Its Applications, vol. 13, Gordon and Breach Science Publishers, New York.
  • Ejsmont W., 2012, Laha-Lukacs properties of some free processes, Electronic Communications in Probability, vol. 17, no. 13, s. 1–8.
  • Ejsmont W., 2013, Noncommutative characterization of free Meixner processes, Electronic Communications in Probability, vol. 18 no. 22, s. 1–12.
  • Ejsmont W., 2014, Characterizations of some free random variables by properties of conditional moments of third degree, Journal of Theoretical Probability, vol. 27, no. 3, s. 915–931.
  • Muraki N., 2001, Monotonic independence, monotonic central limit theorem and monotonic law of small numbers, Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 4, no. 1, s. 39–58.
  • Nica A., Speicher R., 2006, Lectures on the Combinatorics of Free Probability, London Mathematical Society Lecture Notes Series 365, Cambridge University Press, Cambridge.
  • Saitoh N., Yoshida H., 2001, The infinite divisibility and orthogonal polynomials with a constant recursion formula in free probability theory, Probability and Mathematical Statistics, vol. 21, no. 1, s. 159–170.
  • Szpojankowski K., Wesołowski J., 2014, Dual Lukacs regressions for non-commutative variables, Journal of Functional Analysis, vol. 266, no. 1, s. 36–54.
  • Voiculescu D.V., 1985, Symmetries of some reduced free product *-algebras, [w:] Operator Algebras and Their Connections with Topology and Ergodic Theory, Lecture Notes in Mathematics 1132, Springer, Berlin,, s. 556–588,

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.desklight-f9e1967c-c2e1-4f34-a865-166213db1cd3
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