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Volumn 12, Issue , 2007, Pages 44-58

A proof of a non-commutative Central Limit Theorem by the Lindeberg method

Author keywords

Central limit theorem; Free convolution; Free independence; Free probability; Lindeberg method

Indexed keywords


EID: 33847712580     PISSN: None     EISSN: 1083589X     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (5)

References (12)
  • 1
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    • Hari Bercovici, Vittorino Pata, and Philippe Biane. Stable laws and domains of attraction in free probability theory. Annals of Mathematics, 149:1023-1060, 1999. with an appendix by Philippe Biane. MR1709310
    • Hari Bercovici, Vittorino Pata, and Philippe Biane. Stable laws and domains of attraction in free probability theory. Annals of Mathematics, 149:1023-1060, 1999. with an appendix by Philippe Biane. MR1709310
  • 3
    • 33847692883 scopus 로고    scopus 로고
    • Kai Lai Cluing. A Course in Probability Theory. Academic Press, third edition, 2001. MR1796326
    • Kai Lai Cluing. A Course in Probability Theory. Academic Press, third edition, 2001. MR1796326
  • 4
    • 33847706637 scopus 로고    scopus 로고
    • Thierry Fack. Sur la notion de valeur caracteristique. Journal of Operator Theory, 7:307-333, 1982. MR0658616
    • Thierry Fack. Sur la notion de valeur caracteristique. Journal of Operator Theory, 7:307-333, 1982. MR0658616
  • 5
    • 33847743987 scopus 로고    scopus 로고
    • I. C. Gohberg and M. G. Krein. Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Space, 18 of Translations of Mathematical Monographs. American Mathematical Society, 1969. MR0246142
    • I. C. Gohberg and M. G. Krein. Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Space, volume 18 of Translations of Mathematical Monographs. American Mathematical Society, 1969. MR0246142
  • 6
    • 34250956889 scopus 로고    scopus 로고
    • J. W. Lindeberg. Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung. Mathematische Zeitschrift, 15:211-225, 1922. MR1544569
    • J. W. Lindeberg. Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung. Mathematische Zeitschrift, 15:211-225, 1922. MR1544569
  • 7
    • 33847705460 scopus 로고    scopus 로고
    • Roger C. Lyndon and Paul E. Schupp. Combinatorial Group Theory, 89 of Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, New York, 1977. MR0577064
    • Roger C. Lyndon and Paul E. Schupp. Combinatorial Group Theory, volume 89 of Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, New York, 1977. MR0577064
  • 8
    • 33847693700 scopus 로고    scopus 로고
    • A. N. Shiryaev. Probability, 95 of Graduate Text in Mathematics. Springer, second edition, 1995. MR0737192
    • A. N. Shiryaev. Probability, volume 95 of Graduate Text in Mathematics. Springer, second edition, 1995. MR0737192
  • 9
    • 33847743986 scopus 로고    scopus 로고
    • Masamichi Takesaki. Theory of Operator Algebras, 1. Springer-Verlag, New York, 1979. MR0548728
    • Masamichi Takesaki. Theory of Operator Algebras, volume 1. Springer-Verlag, New York, 1979. MR0548728
  • 10
    • 33847762412 scopus 로고    scopus 로고
    • D. Voiculescu. Lectures on free probability theory. In P. Bernard, editor, Lectures on Probability Theory and Statistics, 1738 of Lecture Notes in Mathematics, pages 279-349. Springer. 1998. MR1775641
    • D. Voiculescu. Lectures on free probability theory. In P. Bernard, editor, Lectures on Probability Theory and Statistics, volume 1738 of Lecture Notes in Mathematics, pages 279-349. Springer. 1998. MR1775641
  • 11
    • 33847703451 scopus 로고    scopus 로고
    • Dan Voiculescu. Symmetries of some reduced free product C&z.ast;-algebras. In Lecture Notes in Mathematics, 1132, pages 556-588. Springer-Verlag, New York, 1983. MR0799593
    • Dan Voiculescu. Symmetries of some reduced free product C&z.ast;-algebras. In Lecture Notes in Mathematics, volume 1132, pages 556-588. Springer-Verlag, New York, 1983. MR0799593
  • 12
    • 0000215544 scopus 로고    scopus 로고
    • Dan Voiculescu. Limit laws for random matrices and free products. Inventiones mathematics, 104:201-220, 1991. MR1094052
    • Dan Voiculescu. Limit laws for random matrices and free products. Inventiones mathematics, 104:201-220, 1991. MR1094052


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.