Publications by G. Peccati

Preprints
  1. R. Lachièze-Rey and G. Peccati (2015). New Kolmogorov bounds for functionals of binomial point processes
  2. E. Azmoodeh and G. Peccati (2015). Optimal Berry-Esseen bounds on the Poisson space
  3. S. Bachmann and G. Peccati (2015). Concentration bounds for geometric Poisson functionals: logarithmic Sobolev inequalities revisited.
  4. D. Malicet, I. Nourdin, G. Peccati and G. Poly (2015). Squared chaotic random variables: new moment inequalities with applications.
  5. L. Goldstein, I. Nourdin and G. Peccati (2014). Gaussian phase transitions and conic intrinsic volumes: Steining the Steiner formula.
  6. S. Bourguin, C. Durastanti, D. Marinucci and G. Peccati (2014). Gaussian approximations of non-linear statistics on the sphere
  7. E. Azmoodeh, G. Peccati and G. Poly (2014). The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds.
  8. G. Peccati (2011). The Chen-Stein method for Poisson functionals.

Books
  1. G. Peccati and M.S. Taqqu (2010). Wiener Chaos: Moments, Cumulants and Diagrams. Springer-Verlag. (Errata)
  2. D. Marinucci and G. Peccati (2011). Random Fields on the Sphere. Representation, Limit Theorems and Cosmological Applications. Lecture Notes of the London Mathematical Society, n. 389. Cambridge University Press.
  3. I. Nourdin and G. Peccati (2012). Normal Approximations Using Malliavin Calculus: from Stein's Method to UniversalityCambridge Tracts in Mathematics. Cambridge University Press.
  4. G. Peccati and M. Reitzner (Editors) (2015, to appear). Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometrySpringer-Verlag.

Published and accepted papers
  1. G. Last, G. Peccati and M. Schulte (2015+). Normal approximations on the Poisson space: Mehler's formula, second order Poincaré inequalities and stabilization. To appear in: Probability Theory and Related Fields.
  2. I. Nourdin, D. Nualart and G. Peccati (2015+). Strong asymptotic independence on Wiener chaos. To appear in: Proceedings of the American Mathematical Society.
  3. I. Nourdin, G. Peccati, G. Poly and R. Simone (2015+). Classical and free fourth moment theorems: universality and thresholds. To appear in: Journal of Theoretical Probability.
  4. E. Azmoodeh, G. Peccati and G. Poly (2015+). Convergence towards linear combinations of chi-squared random variables: a Malliavin-based approach. To appear in: Séminaire de Probabilités (Special volume in memory of Marc Yor)
  5. M. Ledoux, I. Nourdin and G. Peccati (2015). Stein's method, logarithmic Sobolev and transport inequalities. Geometric and Functional Analysis 1, 256-306.
  6. I. Nourdin, D. Nualart and G. Peccati (2015+). Quantitative stable limit theorems on the Wiener space. To appear in: The Annals of Probability.
  7. O. El-Dakkak, G. Peccati and I. Prünster (2014). Exchangeable Hoeffding decompositions over finite sets: a characterization and counterexamples. Journal of Multivariate Analysis 131, 51-64.
  8. I. Nourdin, G. Peccati and Y. Swan (2014). Integration by parts and representation of information functionalsProceedings of the 2014 IEEE International Symposium on Information Theory (ISIT), Conference Location: Honolulu, HI. Pages 2217-2221
  9. S. Bourguin and G. Peccati (2014). Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle. The Journal of Functional Analysis, 267(4), 963-997.
  10. G. Peccati (2014). Quantitative CLTs on a Gaussian space: a survey of recent developmentsESAIM: PROCEEDINGS 44, pp. 61-78
  11. S. Bourguin and G. Peccati (2014). Portmanteau inequalities on the Poisson space: mixed limits and multidimensional clustering. The Electronic Journal of Probability. Volume 19, Paper 66 (42 pages)
  12. I. Nourdin, G. Peccati and F. G. Viens (2014). Comparison inequalities on the Wiener spaceStochastic Processes and their Applications 124(4), 1566-1581.
  13. I. Nourdin and G. Peccati (2014). The optimal fourth moment theorem. Proceedings of the American Mathematical Society, to appear.
  14. I. Nourdin, G. Peccati and Y. Swan (2014). Entropy and the fourth moment phenomenonJournal of Functional Analysis 266, 3170-3207.
  15. G. Peccati and Ch. Thaele (2013). Gamma limits and U-statistics on the Poisson space. ALEA 10(1), 525-560.
  16. D. Marinucci and G. Peccati (2013). Mean-square continuity on homogeneous spaces of compact groups. Electronic Communications in Probability, Vol. 18, paper 37, 1-10.
  17. R. Lachièze-Rey and G. Peccati (2013). Fine Gaussian fluctuations on the Poisson space, II: rescaled kernels, marked processes and geometric U-statistics. Stochastic Processes and their Applications 123(12), 4186-4218.
  18. C. Durastanti, D. Marinucci and G. Peccati (2013). Normal approximation for wavelets coefficients on spherical Poisson fields. Journal of Mathematical Analysis and Applications  409(1), 212-227.
  19. G. Peccati and C. Zheng (2013). Universal Gaussian fluctuations on the discrete Poisson chaos. To appear in: Bernoulli.
  20. R. Lachièze-Rey and G. Peccati (2013). Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and random geometric graphs. The Electronic Journal of Probability, 18(32), 1-35.
  21. I. Nourdin and G. Peccati (2013). Poisson approximations on the free Wigner chaos. The Annals of Probability 41(4), 2709-2723.
  22. H. Biermé, A. Bonami, I. Nourdin and G. Peccati (2012). Optimal Berry-Esseen rates on the Wiener space: the barrier of third and fourth cumulants. ALEA, 9(2), 473-500.
  23. I. Nourdin, G. Peccati and R. Speicher (2013). Multidimensional semicircular limits on the free Wigner chaos. In the volume: Ascona Proceedings 2011, Progress in Probability 67, 211-221.
  24. T. Kemp, I. Nourdin, G. Peccati and R. Speicher (2012). Wigner chaos and the fourth moment. The Annals of Probability 40(4), 1577-1635.
  25. I. Nourdin, G. Peccati and M. Podolskij (2011). Quantitative Breuer-Major theorems. Stochastic Processes and their Applications 121, 793-812
  26. I. Nourdin, G. Peccati and G. Reinert (2010). Stein's method and stochastic analysis of Rademacher sequences. The Electronic Journal of Probability, 15; Paper 55: p. 1703-1742 (Electronic)
  27. G. Peccati and C. Zheng (2010). Multi-dimensional Gaussian fluctuations on the Poisson spaceThe Electronic Journal of Probability, 15; Paper 48: p. 1487-1527 (Electronic)
  28. I. Nourdin and G. Peccati (2010). Universal Gaussian fluctuations of non-Hermitian matrix ensembles: from weak convergence to almost sure CLTs.  ALEA 7, 341-375 (Electronic)
  29. G. Peccati and J.-R. Pycke (2010). Hoeffding spaces and Specht modules. To appear in: ESAIM, Probability and Statistics (Special Volume in Honor of Marc Yor)
  30. I. Nourdin, G. Peccati and G. Reinert (2010). Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos. The Annals of Probability 38(5), 1947-1985
  31. D. Marinucci and G. Peccati (2010). Ergodicity and Gaussianity for Spherical Random Fields. Journal of Mathematical Physics 51, 043301
  32. D. Marinucci and G. Peccati (2010). Representations of SO(3) and angular polyspectra. The Journal of Multivariate Analysis 101, 77-100
  33. I. Nourdin and G. Peccati (2010). Stein's method and exact Berry-Esséen asymptotics for functionals of Gaussian fields. The Annals of Probability 37(6), 2231-2261
  34. I. Nourdin and G. Peccati (2010). Cumulants on the Wiener space. Journal of Functional Analysis 258, 3775-3791
  35. I. Nourdin and G. Peccati (2010). Stein's method meets Malliavin calculus: a short survey with new estimates. In the volume: Recent Advances in Stochastic Dynamics and Stochastic Analysis, World Scientific
  36. G. Peccati, J.-L. Solé, M.S. Taqqu and F. Utzet (2010). Stein's method and normal approximation of Poisson functionals. The Annals of Probability 38(2), 443-478
  37. I. Nourdin, G. Peccati and A. Reveillac (2010). Multivariate normal approximation using Stein's method and Malliavin calculus.  Annales de l'Institut H. Poincaré (B) - Probability and Statistics, 46(1), 45-58
  38. G. Peccati and J.-R. Pycke (2010). Decompositions of stochastic processes based on irreducible group representations. Theory of Probability and Applications 54(2), 217-245
  39. D. Marinucci and G. Peccati (2010). Group representations and high-resolution central limit theorems for subordinated spherical random fields. Bernoulli 16(3), 798-824
  40. P. De Blasi, G. Peccati and I. Pruenster (2010). On the asymptotic behaviour of random cumulative hazards. In: JSM Proceedings, 1063-1074
  41. J.-C. Breton, I. Nourdin and G. Peccati (2009). Exact confidence intervals for the Hurst parameter of a fractional Brownian motion. The Electronic Journal of Statistics 3, 416-425 (electronic)
  42. I. Nourdin, G. Peccati and G. Reinert (2009). Second order Poincaré inequalities and CLTs on Wiener space. Journal of Functional Analysis 257, 593-609 (NB: The latest version on the ArXiv has a couple of typos corrected with respect to the published version)
  43. I. Nourdin and G. Peccati (2009). Non-central convergence of multiple integrals. The Annals of Probability 37(4), 1412–1426
  44. S. Darses, I. Nourdin and G. Peccati (2009). Stochastic derivatives for Gaussian and shifted Gaussian processes.  Stochastics 81(1), 79-97
  45. P. De Blasi, G. Peccati and I. Prünster (2009). Asymptotics for posterior hazards. The Annals of Statistics 37(4), 1906-1945
  46. I. Nourdin and G. Peccati (2009). Stein's method on Wiener chaos. Probability Theory and Related Fields 145(1), 75-118
  47. I. Nourdin and G. Peccati (2008). Weighted variations of iterated Brownian motion. The Electronic Journal of Probability 13, n. 43, 1229-1256 (Electronic)
  48. G. Peccati and M.S. Taqqu (2008). Limit theorems for multiple stochastic integrals. ALEA 4, 393-413
  49. G. Peccati and M.S. Taqqu (2008). Stable convergence of multiple Wiener-Itô integrals. The Journal of Theoretical Probability 21(3), 527-570
  50. G. Peccati and M.S. Taqqu (2008). Central limit theorems for double Poisson integrals. Bernoulli 14(3), 791-821
  51. O. El-Dakkak and G. Peccati (2008). Hoeffding decompositions and urn sequences. The Annals of Probability 36(6), 2280-2310
  52. G. Peccati and I. Prünster (2008). Linear and quadratic functionals of random hazard rates: an asymptotic analysis . The Annals of Applied Probability 18, 1910-1943
  53. G. Peccati and M. Yor (2008). Burkholder's submartingales from a stochastic calculus perspective. The Illinois Journal of Mathematics, 52(3), 815-824
  54. D. Marinucci and G. Peccati (2008). High-frequency asymptotics for subordinated stationary fields on an Abelian compact group. Stochastic Processes and their Applications 118(4), 585-613
  55. G. Peccati (2008). Multiple integral representation for functionals of Dirichlet processes. Bernoulli 14(1), 91-124
  56. G. Peccati and C.A. Tudor (2007). Anticipating integrals and martingales on the Poisson space. Random Operators and Stochastic Equations 15, 327-352
  57. G. Peccati (2007). Gaussian approximations of multiple integrals. Electronic Communications in Probability 12, 350-364 (Electronic)
  58. G. Peccati and M.S. Taqqu (2007). Stable convergence of generalized L² stochastic integrals and the principle of conditioning. The Electronic Journal of Probability, 12, 447-480, n. 15 (Electronic)
  59. G. Peccati, M. Thieullen and C.A. Tudor (2006). Martingale structure of Skorohod integral processes. The Annals of Probability, 34(3), 1217-1239
  60. P. Deheuvels, G. Peccati and M. Yor (2006) On quadratic functionals of the Brownian sheet and related processes. Stochastic Processes and their Applications 116, 493-538
  61. G. Peccati and M. Yor (2005). Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections. In: Approximation and Probability, Banach Center Publications 72. Warsaw, Poland
  62. D. Nualart and G. Peccati (2005). Central limit theorems for sequences of multiple stochastic integrals. The Annals of Probability, 33(1), 177-193
  63. G. Peccati and C.A. Tudor (2004). Gaussian limits for vector-valued multiple stochastic integrals. Séminaire de Probabilités XXXVIII, 247-262
  64. G. Peccati (2004). Weak convergence to Ocone martingales: a remark. Electronic Communications in Probability 9, 172-174
  65. G. Peccati (2004). Anticipative stochastic integration based on time-space chaos. Stochastic Processes and Their Applications, 112(2), 331-355
  66. G. Peccati (2004). Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observations. The Annals of Probability, 32 (3A), 1796-1829
  67. G. Peccati and M. Yor (2004). Four limit theorems for quadratic functionals of Brownian motion and Brownian bridge. Asymptotic Methods in Stochastics, AMS, Fields Institute Communication Series, 75-87
  68. G. Peccati and M. Yor (2004). Hardy's inequality in L²([0,1]) and principal values of Brownian local times. Asymptotic Methods in Stochastics, AMS, Fields Institute Communications Series, 49-74
  69. G. Peccati (2003). Hoeffding decompositions for exchangeable sequences and chaotic representation for functionals of Dirichlet processes. C.R.A.S. - Mathématiques, Vol. 336/10, 845-850
  70. G. Peccati (2003). Explicit formulae for time-space Brownian chaos. Bernoulli, 9, 25-48
  71. G. Peccati (2001). On the convergence of multiple random integrals. Studia Sc. Mat. Hungarica, 37, 429-470
  72. G. Peccati (2001). A representation result for time-space Brownian chaos. Annales de l'Institut H. Poincaré (PR), 37, 607-625
  73. G. Peccati (1998). Some results about Itô processe with jumps. Atti del XXIII Convegno AMASES.

Other papers
  1. G. Peccati (2004). A time-space hedging theory
  2. G. Peccati and M.S. Taqqu (2008). Moments, cumulants and diagram formulae for functionals of random measures.
  3. I. Nourdin and G. Peccati (2009). Universal Gaussian fluctuations of non-Hermitian matrix ensembles.
  4. From Wiener to time-space chaos, via conditioned Gaussian measures (2001), Preprint n. 648 du Laboratoire de Probabilités de l'Université Paris VI
  5. Sui fondamenti della probabilità (Italian; 2002), La scuola classica di Cremona, 283-292


Nota

Thanks to a paper co-written with Paul Deheuvels (and Marc Yor), my Erdös Number is 2, see also here.