Free Access
Volume 20, 2016
Page(s) 293 - 308
Published online 05 August 2016
  1. M. Anshelevich, S.T. Belinschi, M. Bozejko and F. Lehner, Free infinite divisibility for q-Gaussians. Math. Res. Lett. 17 (2010) 905–916. [CrossRef] [MathSciNet] [Google Scholar]
  2. O. Arizmendi, Convergence of the fourth moment and infinite divisibility. Probab. Math. Stat. 33 (2013) 201–212. [Google Scholar]
  3. O. Arizmendi and A. Jaramillo, Convergence of the fourth moment and infinite divisibility: quantitative estimates. Electron. Commun. Probab. 19 (2014) 1–12. [CrossRef] [MathSciNet] [Google Scholar]
  4. O. Arizmendi and V. Pérez-Abreu, On the non-classical infinite divisibility of power semicircle distributions. Commun. Stochastic Anal. 4 (2010) 161–178. [Google Scholar]
  5. E. Azmoodeh, S. Campese and G. Poly, Fourth Moment Theorems for Markov Diffusion Generators. J. Funct. Anal. 266 (2014) 2341–2359. [CrossRef] [MathSciNet] [Google Scholar]
  6. E. Azmoodeh, D. Malicet, G. Mijoule and G. Poly, Generalization of the Nualart-Peccati criterion. Ann. Probab. 44 (2016) 924–954. [CrossRef] [MathSciNet] [Google Scholar]
  7. B. Bhattacharya, P. Diaconis and S. Mukherjee, Universal limit theorems in graph coloring problems with connections to extremal combinatorics. Preprint arXiv:1310.2336 (2014). [Google Scholar]
  8. P. Biane and R. Speicher, Stochastic analysis with respect to free Brownian motion and analysis on Wigner space. Probab. Theory Relat. Fields 112 (1998) 373–409. [CrossRef] [Google Scholar]
  9. S. Bourguin, Poisson convergence on the free Poisson algebra. Bernoulli 21 (2015) 2139–2156. [CrossRef] [MathSciNet] [Google Scholar]
  10. S. Bourguin and G. Peccati, Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle. J. Funct. Anal. 267 (2013) 963–997. [CrossRef] [Google Scholar]
  11. S. Campese, I. Nourdin, G. Peccati and G. Poly, Multivariate Gaussian approximation on Markov chaoses. Preprint arXiv:1510.02105 (2015). [Google Scholar]
  12. L.H.Y. Chen, Stein meets Malliavin in Normal Approximation. Acta Math. Vietnamica 40 (2015) 205. [CrossRef] [Google Scholar]
  13. L.H.Y. Chen and G. Poly, Stein’s method, Malliavin calculus, Dirichlet forms and the fourth moment theorem. Festschrift Masatoshi Fukushima. Edited by Z.-Q. Chen, N. Jacob, M. Takeda and T. Uemura. In vol. 17 of Interdiscipl. Math. Sci. (2015) 107–130. [Google Scholar]
  14. P. de Jong, A central limit theorem for generalized multilinear forms. J. Multivar. Anal. 34 (1987) 275–289. [Google Scholar]
  15. A. Deya and I. Nourdin, Convergence of Wigner integrals to the Tetilla law. ALEA, Lat. Am. J. Probab. Math. Stat. 9 (2012) 101–127. [MathSciNet] [Google Scholar]
  16. A. Deya and I. Nourdin, Invariance principles for homogeneous sums of free random variables. Bernoulli 20 (2013) 586–603. [CrossRef] [Google Scholar]
  17. A. Deya, S. Norredine and I. Nourdin, Fourth Moment Theorem and q-Brownian Motion. Commun. Math. Phys. 321 (2013) 113–134. [CrossRef] [Google Scholar]
  18. P. Eichelsbacher and C. Thäle, New Berry-Esseen bounds for non-linear functionals of Poisson random measures. Electron. J. Probab. 19 (2014) 1–25. [CrossRef] [MathSciNet] [Google Scholar]
  19. T. Fissler and C. Thäle, A four moment theorem for Gamma limits on a Poisson chaos. Preprint arXiv:1502.01568 (2015). [Google Scholar]
  20. T. Kemp, I. Nourdin, G. Peccati and R. Speicher, Wigner Chaos and the fourth moment. Ann. Probab. 40 (2011) 1577–1635. [CrossRef] [Google Scholar]
  21. R. Lachiéze-Rey and G. Peccati, Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs. Electron. J. Probab. 18 (2013) 1–32. [CrossRef] [MathSciNet] [Google Scholar]
  22. E. Mossel, Gaussian bounds for noise correlation of functions. Geometric Funct. Anal. 19 (2010) 1713–1756. [CrossRef] [Google Scholar]
  23. E. Mossel, R. O’Donnell and K. Oleszkiewicz, Noise stability of functions with low influences: invariance and optimality. Ann. Math. 171 (2010) 295–341. [CrossRef] [MathSciNet] [Google Scholar]
  24. A. Nica and R. Speicher, Lectures on the Combinatorics of Free Probability. Cambridge University Press (1990). [Google Scholar]
  25. I. Nourdin and G. Peccati, Noncentral convergence of multiple integrals. Ann. Probab. 37 (2009) 1412–1426. [CrossRef] [MathSciNet] [Google Scholar]
  26. I. Nourdin and G. Peccati, Normal approximations with Malliavin calculus: from Stein’s method to universality. Cambridge Tracts in Mathematics. Cambridge University Press (2012). [Google Scholar]
  27. I. Nourdin and G. Peccati. Poisson approximations on the free Wigner chaos. Ann. Probab. 41 (2013) 2709–2723. [CrossRef] [MathSciNet] [Google Scholar]
  28. I. Nourdin, G. Peccati and G. Reinert, Invariance principles for homogeneous sums: universality of Gaussian Wiener Chaos. Ann. Probab. 38 (2010) 1947–1985. [CrossRef] [MathSciNet] [Google Scholar]
  29. I. Nourdin, G. Peccati and A. Reveillac, Multivariate normal approximation using Stein’s method and Malliavin calculus. Ann. Inst. Henri Poincaré, Probab. Stat. 46 (2010) 45–58. [CrossRef] [MathSciNet] [Google Scholar]
  30. I. Nourdin, G. Peccati and R. Speicher, Multidimensional semicircular limits on the free Wigner Chaos. Ascona Proceedings 2011. In vol. 67 of Progress in Probability (2013) 211–221. [Google Scholar]
  31. I. Nourdin, G. Peccati and Y. Swan, Entropy and the fourth moment phenomenon. J. Funct. Anal. 266 (2014) 3170–3207. [CrossRef] [MathSciNet] [Google Scholar]
  32. I. Nourdin, G. Peccati, G. Poly and R. Simone, Classical and free fourth moment theorems: universality and thresholds. J. Theoret. Probab. 29 (2016) 653–680. [CrossRef] [MathSciNet] [Google Scholar]
  33. D. Nualart and G. Peccati, Central limit theorems for sequences of multiple stochastic integrals. Ann. Probab. 33 (2005) 177–193. [CrossRef] [MathSciNet] [Google Scholar]
  34. G. Peccati, Quantitative CLTs on a Gaussian space: a survey of recent developments. ESAIM: Proc. Suv. 44 (2014) 61–78. [CrossRef] [EDP Sciences] [Google Scholar]
  35. G. Peccati and M.S. Taqqu, Wiener Chaos: Moments, Cumulants and Diagrams. Springer-Verlag (2010). [Google Scholar]
  36. G. Peccati and Ch. Thaele, Gamma limits and U-statistics on the Poisson space. ALEA, Lat. Am. J. Probab. Math. Stat. 10 (2013) 525–560. [MathSciNet] [Google Scholar]
  37. G. Peccati and C. Tudor, Gaussian limits for vector-valued multiple stochastic integrals. In vol. XXXVIII, Séminaire de Probabilités (2005) 247–262. [Google Scholar]
  38. G. Peccati and C. Zheng, Universal Gaussian fluctuations on the discrete Poisson chaos. Bernoulli 20 (2013) 697–715. [Google Scholar]
  39. G. Peccati, J.L. Solé, M.S. Taqqu and F. Utzet, Stein’s method and normal approximation of Poisson functionals. Ann. Probab. 38 (2010) 443–478. [CrossRef] [MathSciNet] [Google Scholar]
  40. R. Simone, Universality for free homogeneous sums in every dimension. ALEA, Lat. Am. J. Probab. Math. Stat. 12 (2015) 213–244. [MathSciNet] [Google Scholar]
  41. D. Voiculescu, Symmetries of some reduced free product C-algebras. Operator algebras and their connection with topology and ergodic theory. Vol. 1132 of Lect. Notes Math. Springer (1985) 556–588. [Google Scholar]

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