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2015 | 12(16) | 55-60
Article title

Remarks on Wigner’s semicircle law

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EN
Abstracts
EN
Ejsmont [2014] has shown that families of free Meixner distributions can be characterized by the conditional moments of polynomial functions of degree 3. In this paper, we will give other characterizations of the free normal distribution which are formulated in a similar spirit.
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55-60
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References
  • Biane P. (1998). Processes with free increments. Mathematische Zeitschrift 227(1). Pp. 143-174.
  • Bożejko M., Bryc W. (2006). On a class of free Lévy laws related to a regression problem. Journal of Functional Analysis 236. Pp. 59-77.
  • Ejsmont W. (2014). Characterizations of some free random variables by properties of conditional moments of third degree polynomials. Journal of Theoretical Probability 27 (3). Pp. 915-931.
  • Nica A., Speicher R. (2006). Lectures on the Combinatorics of Free Probability. London Mathematical Society Lecture Notes Series 365. Cambridge University Press.
  • Speicher R. (1997). Free probability theory and non-crossing partitions. Séminaire Lotharingien de Combinatoire B39c. Pp. 38. (electronic)
  • http://www.emis.ams.org/journals/SLC/wpapers/s39speicher.pdf.
  • Takesaki M. (1972). Conditional expectations in von Neumann algebras. Journal of Functional Analysis 9. Pp. 306-321.
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Publication order reference
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YADDA identifier
bwmeta1.element.desklight-cf503e30-9b93-420b-8d9b-d38bceb2403b
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