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Volumn 41, Issue 4, 2013, Pages 2709-2723

Poisson approximations on the free wigner chaos

Author keywords

Catalan numbers; Contractions; Free Brownian motion; Free cumulants; Free Poisson distribution; Free probability; Marchenko Pastur; Noncentral limit theorems; Noncrossing partitions; Riordan numbers; Semicircular distribution; Wigner chaos

Indexed keywords


EID: 84881514981     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/12-AOP815     Document Type: Article
Times cited : (16)

References (16)
  • 1
    • 39449098318 scopus 로고    scopus 로고
    • Spectral Analysis of Large Dimensional Random Matrices, 2nd ed
    • Springer, New York. MR2567175
    • Bai, Z. and Silverstein, J. W. (2010). Spectral Analysis of Large Dimensional Random Matrices, 2nd ed. Springer, New York. MR2567175
    • (2010)
    • Bai, Z.1    Silverstein, J.W.2
  • 2
    • 0003124224 scopus 로고    scopus 로고
    • Catalan, Motzkin, and Riordan numbers
    • MR1691863
    • Bernhart, F. R. (1999). Catalan, Motzkin, and Riordan numbers. Discrete Math. 204 73-112. MR1691863
    • (1999) Discrete Math. , vol.204 , pp. 73-112
    • Bernhart, F.R.1
  • 3
    • 0040427874 scopus 로고    scopus 로고
    • Stochastic calculus with respect to free Brownian motion and analysis on Wigner space
    • MR1660906
    • Biane, P. and Speicher, R. (1998). Stochastic calculus with respect to free Brownian motion and analysis on Wigner space. Probab. Theory Related Fields 112 373-409. MR1660906
    • (1998) Probab. Theory Related Fields , vol.112 , pp. 373-409
    • Biane, P.1    Speiche, R.2
  • 4
  • 5
    • 84866040106 scopus 로고    scopus 로고
    • Convergence of Wigner integrals to the tetilla law
    • MR2893412
    • Deya, A. and Nourdin, I. (2012). Convergence of Wigner integrals to the tetilla law. ALEA Lat. Am. J. Probab. Math. Stat. 9 101-127. MR2893412
    • (2012) ALEA Lat. Am. J. Probab. Math. Stat. , vol.9 , pp. 101-127
    • Deya, A.1    Nourdin, I.2
  • 6
    • 0005141929 scopus 로고    scopus 로고
    • The Semicircle Law, Free Random Variables and Entropy
    • Mathematical Surveys and Monographs 77., Providence, RI. MR1746976
    • Hiai, F. and Petz, D. (2000). The Semicircle Law, Free Random Variables and Entropy. Mathematical Surveys and Monographs 77. Amer. Math. Soc., Providence, RI. MR1746976
    • (2000) Amer. Math. Soc.
    • Hiai, F.1    Petz, D.2
  • 7
    • 84866037944 scopus 로고    scopus 로고
    • Wigner chaos and the fourth moment
    • MR2978133
    • Kemp, T.,Nourdin, I., Peccati, G. and Speicher, R. (2012).Wigner chaos and the fourth moment. Ann. Probab. 40 1577-1635. MR2978133
    • (2012) Ann. Probab. , vol.40 , pp. 1577-1635
    • Kemp, T.1    Nourdin, I.2    Peccati, G.3    Speicher, R.4
  • 8
    • 34548010063 scopus 로고    scopus 로고
    • Lectures on the Combinatorics of Free Probability
    • London Mathematical Society Lecture Note Series 335. Cambridge Univ. Press, Cambridge. MR2266879
    • Nica, A. and Speicher, R. (2006). Lectures on the Combinatorics of Free Probability. London Mathematical Society Lecture Note Series 335. Cambridge Univ. Press, Cambridge. MR2266879
    • (2006)
    • Nica, A.1    Speicher, R.2
  • 9
    • 84877069750 scopus 로고    scopus 로고
    • A webpage on Stein's method, Malliavin calculus and related topics
    • Available at
    • Nourdin, I. (2012). A webpage on Stein's method, Malliavin calculus and related topics. Available at http://www.iecn.u-nancy.fr/~nourdin/steinmalliavin.htm.
    • (2012)
    • Nourdin, I.1
  • 10
    • 80053088070 scopus 로고    scopus 로고
    • Yet another proof of the Nualart-Peccati criterion
    • MR2831085
    • Nourdin, I. (2011). Yet another proof of the Nualart-Peccati criterion. Electron. Commun. Probab. 16 467-481. MR2831085
    • (2011) Electron. Commun. Probab. , vol.16 , pp. 467-481
    • Nourdin, I.1
  • 11
    • 64249132864 scopus 로고    scopus 로고
    • Noncentral convergence of multiple integrals
    • MR2546749
    • Nourdin, I. and Peccati, G. (2009). Noncentral convergence of multiple integrals. Ann. Probab. 37 1412-1426. MR2546749
    • (2009) Ann. Probab. , vol.37 , pp. 1412-1426
    • Nourdin, I.1    Peccati, G.2
  • 13
    • 85123568761 scopus 로고    scopus 로고
    • Stein's method meets Malliavin calculus: A short survey with new estimates
    • In Recent Development in Stochastic Dynamics and Stochastic Analysis. World Sci. Publ., Hackensack, NJ. MR2807823
    • Nourdin, I. and Peccati, G. (2010). Stein's method meets Malliavin calculus: A short survey with new estimates. In Recent Development in Stochastic Dynamics and Stochastic Analysis. Interdiscip. Math. Sci. 8 207-236. World Sci. Publ., Hackensack, NJ. MR2807823
    • (2010) Interdiscip. Math. Sci. , vol.8 , pp. 207-236
    • Nourdin, I.1    Peccati, G.2
  • 14
    • 84866049668 scopus 로고    scopus 로고
    • Normal Approximations with Malliavin Calculus: From Stein's Method to Universality
    • Cambridge Tracts in Mathematics 192. Cambridge Univ. Press, Cambridge. MR2962301
    • Nourdin, I. and Peccati, G. (2012). Normal Approximations with Malliavin Calculus: From Stein's Method to Universality. Cambridge Tracts in Mathematics 192. Cambridge Univ. Press, Cambridge. MR2962301
    • (2012)
    • Nourdin, I.1    Peccati, G.2
  • 15
    • 14944377936 scopus 로고    scopus 로고
    • Central limit theorems for sequences of multiple stochastic integrals
    • MR2118863
    • Nualart, D. and Peccati, G. (2005). Central limit theorems for sequences of multiple stochastic integrals. Ann. Probab. 33 177-193. MR2118863
    • (2005) Ann. Probab. , vol.33 , pp. 177-193
    • Nualart, D.1    Peccati, G.2
  • 16
    • 78649700173 scopus 로고    scopus 로고
    • Wiener Chaos: Moments, Cumulants and Diagrams: A Survey With Computer Implementation
    • Bocconi & Springer Series 1. Springer, Milan. MR2791919
    • Peccati, G. and Taqqu, M. S. (2011). Wiener Chaos: Moments, Cumulants and Diagrams: A Survey With Computer Implementation. Bocconi & Springer Series 1. Springer, Milan. MR2791919
    • (2011)
    • Peccati, G.1    Taqqu, M.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.