The free analogue of noncentral chi-square distributions and symmetric quadratic forms in free random variables

Mathematische Zeitschrift

Volumn 230, Issue 1, 1999, Pages 63-77

  Hiwatashi, Osamu ^a   Kuroda, Tomoko ^b   Nagisa, Masaru ^a   Yoshida, Hiroaki ^b  

^a CHIBA UNIVERSITY   (Japan)

^b OCHANOMIZU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033484777     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004689     Document Type: Article

References (10)

1. Bercovici, H., Voiculescu, D.: Superconvergence to the central limit and failure of the Cramér theorem for free random variables, Probab. Theory Relat. Fields 102, 215-222 (1995)
2. Feller, W.: An Introduction to Probability Theory and Its Applications, vol.II, 3rd ed. New York, John Wiley, 1973
3. *-probability space, (Preprint 1997)
4. Kagan, A., Linnik, Y., Rao, C.: Characterization Problems in Mathematical Statistics, New York, John Wiley, 1973.
5. Nica, A.: R - transform of free joint distributions and non-crossing partitions, J. Funct. Anal. 135, 271-296 (1996)
6. Nica, A., Speicher, R., Voiculescu, D.: On the multiplication of free N - tuples of noncommutative random variables, Appendix: Alternative proofs for the type II free Poisson variables and for the free compression results, Amer. J. Math. 118, 799-837 (1996)
7. Speicher, R.: A new example of 'Independence' and 'White Noise', Probab. Theory Relat. Fields 84, 141-159 (1990)
8. Voiculescu, D., Dykema, K., Nica, A. : Free random variables, CMR Monograph Ser., vol. 1, AMS, 1992
9. *-algebras, Operator algebras and Their Connections with Topology and Ergodic Theory, Lecture Note in Mathematics, vol. 1132, Berlin Heidelberg New York, Springer, 1985, pp. 556-588
10. Voiculescu, D.: Addition of certain non-commutative random variables, J. Funct. Anal. 66, 323-235 (1986)