Publications by G. Peccati

Preprints
  1. Ch. Döbler and G. Peccati (2016). The Gamma Stein equation and de Jong type theorems
  2. F. Dalmao, I. Nourdin, G. Peccati and M. Rossi (2016). Phase singularities in complex arithmetic random waves.
  3. E. Azmoodeh and G. Peccati (2015). Optimal Berry-Esseen bounds on the Poisson space
  4. 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. (This book won the 2015 FNR Award for outstanding scientific publication).
  4. G. Peccati and M. Reitzner (Editors) (2016). Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometrySpringer-Verlag.

Published and accepted papers
  1. M. Ledoux, I. Nourdin and G. Peccati (2016). A Stein deficit for the logarithmic Sobolev inequality. To appear in: Science China Mathematics
  2. Ch. Döbler and G. Peccati (2016). Quantitative de Jong theorems in any dimension. To appear in: Electronic Journal of Probability
  3. G. Mijoule, G. Peccati and Y. Swan (2016). On the rate of convergence in de Finetti's representation theorem. To appear in: ALEA
  4. S. Campese, I. Nourdin, G. Peccati and G. Poly (2016). Multivariate Gaussian approximation on Markov chaoses. To appear in: Electronic Communications in Probability
  5. D. Marinucci, G. Peccati, M. Rossi and I. Wigman (2016+). Non-universality of nodal length distribution for arithmetic random waves. To appear in: Geometric and Functional Analysis
  6. R. Lachièze-Rey and G. Peccati (2016+). New Kolmogorov bounds for functionals of binomial point processes. To appear in: The Annals of Applied Probability
  7. I. Nourdin, G. Peccati, G. Poly and R. Simone (2016+). Multidimensional limit theorems for homogeneous sums: a general transfer principle. To appear in: ESAIM P&S
  8. E. Azmoodeh, G. Peccati and G. Poly (2016+). The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds. To appear in: ALEA
  9. L. Goldstein, I. Nourdin and G. Peccati (2016+). Gaussian phase transitions and conic intrinsic volumes: Steining the Steiner formula. To appear in: The Annals of Applied Probability
  10. S. Bachmann and G. Peccati (2016). Concentration bounds for geometric Poisson functionals: logarithmic Sobolev inequalities revisited. The Electronic Journal of Probability, 21, paper no. 6, 44 pages.
  11. S. Bourguin, C. Durastanti, D. Marinucci and G. Peccati (2016). Gaussian approximations of non-linear statistics on the sphere. To appear in: Journal of Mathematical Analysis and Applications
  12. D. Malicet, I. Nourdin, G. Peccati and G. Poly (2016). Squared chaotic random variables: new moment inequalities with applicationsJournal of Functional Analysis, 270(2), 649-670.
  13. G. Last, G. Peccati and M. Schulte (2016). Normal approximations on the Poisson space: Mehler's formula, second order Poincaré inequalities and stabilization. To appear in: Probability Theory and Related Fields.
  14. I. Nourdin, D. Nualart and G. Peccati (2016). Strong asymptotic independence on Wiener chaos. Proceedings of the American Mathematical Society 144(2), 875-886.
  15. I. Nourdin, G. Peccati, G. Poly and R. Simone (2016). Classical and free fourth moment theorems: universality and thresholds. To appear in: Journal of Theoretical Probability.
  16. E. Azmoodeh, G. Peccati and G. Poly (2015). Convergence towards linear combinations of chi-squared random variables: a Malliavin-based approach. In: Séminaire de Probabilités XLVII (Special volume in memory of Marc Yor), 339-367.
  17. M. Ledoux, I. Nourdin and G. Peccati (2015). Stein's method, logarithmic Sobolev and transport inequalities. Geometric and Functional Analysis 25, 256-306.
  18. I. Nourdin and G. Peccati (2015). The optimal fourth moment theoremProceedings of the American Mathematical Society, 143(7), 3123-3133.
  19. I. Nourdin, D. Nualart and G. Peccati (2016). Quantitative stable limit theorems on the Wiener space. To appear in: The Annals of Probability.
  20. 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.
  21. 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
  22. 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.
  23. G. Peccati (2014). Quantitative CLTs on a Gaussian space: a survey of recent developmentsESAIM: PROCEEDINGS 44, pp. 61-78
  24. S. Bourguin and G. Peccati (2014). Portmanteau inequalities on the Poisson space: mixed limits and multidimensional clusteringThe Electronic Journal of Probability. Volume 19, Paper 66 (42 pages)
  25. I. Nourdin, G. Peccati and F. G. Viens (2014). Comparison inequalities on the Wiener spaceStochastic Processes and their Applications 124(4), 1566-1581.
  26. I. Nourdin, G. Peccati and Y. Swan (2014). Entropy and the fourth moment phenomenonJournal of Functional Analysis 266, 3170-3207.
  27. G. Peccati and Ch. Thaele (2013). Gamma limits and U-statistics on the Poisson space. ALEA 10(1), 525-560.
  28. 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.
  29. 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.
  30. 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.
  31. G. Peccati and C. Zheng (2014). Universal Gaussian fluctuations on the discrete Poisson chaos. Bernoulli 20(2), 697-715.
  32. 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.
  33. I. Nourdin and G. Peccati (2013). Poisson approximations on the free Wigner chaos. The Annals of Probability 41(4), 2709-2723.
  34. 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.
  35. 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.
  36. T. Kemp, I. Nourdin, G. Peccati and R. Speicher (2012). Wigner chaos and the fourth moment. The Annals of Probability 40(4), 1577-1635.
  37. I. Nourdin, G. Peccati and M. Podolskij (2011). Quantitative Breuer-Major theorems. Stochastic Processes and their Applications 121, 793-812
  38. 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)
  39. 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)
  40. 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)
  41. 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)
  42. 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
  43. D. Marinucci and G. Peccati (2010). Ergodicity and Gaussianity for Spherical Random FieldsJournal of Mathematical Physics 51, 043301
  44. D. Marinucci and G. Peccati (2010). Representations of SO(3) and angular polyspectra. The Journal of Multivariate Analysis 101, 77-100
  45. 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
  46. I. Nourdin and G. Peccati (2010). Cumulants on the Wiener space. Journal of Functional Analysis 258, 3775-3791
  47. 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
  48. 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
  49. 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
  50. 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
  51. D. Marinucci and G. Peccati (2010). Group representations and high-resolution central limit theorems for subordinated spherical random fields. Bernoulli 16(3), 798-824
  52. P. De Blasi, G. Peccati and I. Pruenster (2010). On the asymptotic behaviour of random cumulative hazards. In: JSM Proceedings, 1063-1074
  53. 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)
  54. 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)
  55. I. Nourdin and G. Peccati (2009). Non-central convergence of multiple integrals. The Annals of Probability 37(4), 1412–1426
  56. S. Darses, I. Nourdin and G. Peccati (2009). Stochastic derivatives for Gaussian and shifted Gaussian processes.  Stochastics 81(1), 79-97
  57. P. De Blasi, G. Peccati and I. Prünster (2009). Asymptotics for posterior hazards. The Annals of Statistics 37(4), 1906-1945
  58. I. Nourdin and G. Peccati (2009). Stein's method on Wiener chaos. Probability Theory and Related Fields 145(1), 75-118
  59. I. Nourdin and G. Peccati (2008). Weighted variations of iterated Brownian motion. The Electronic Journal of Probability 13, n. 43, 1229-1256 (Electronic)
  60. G. Peccati and M.S. Taqqu (2008). Limit theorems for multiple stochastic integrals. ALEA 4, 393-413
  61. G. Peccati and M.S. Taqqu (2008). Stable convergence of multiple Wiener-Itô integrals. The Journal of Theoretical Probability 21(3), 527-570
  62. G. Peccati and M.S. Taqqu (2008). Central limit theorems for double Poisson integrals. Bernoulli 14(3), 791-821
  63. O. El-Dakkak and G. Peccati (2008). Hoeffding decompositions and urn sequences. The Annals of Probability 36(6), 2280-2310
  64. 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
  65. G. Peccati and M. Yor (2008). Burkholder's submartingales from a stochastic calculus perspective. The Illinois Journal of Mathematics52(3), 815-824
  66. 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
  67. G. Peccati (2008). Multiple integral representation for functionals of Dirichlet processes. Bernoulli 14(1), 91-124
  68. G. Peccati and C.A. Tudor (2007). Anticipating integrals and martingales on the Poisson space. Random Operators and Stochastic Equations 15, 327-352
  69. G. Peccati (2007). Gaussian approximations of multiple integrals. Electronic Communications in Probability 12, 350-364 (Electronic)
  70. 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)
  71. G. Peccati, M. Thieullen and C.A. Tudor (2006). Martingale structure of Skorohod integral processes. The Annals of Probability, 34(3), 1217-1239
  72. 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
  73. 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
  74. D. Nualart and G. Peccati (2005). Central limit theorems for sequences of multiple stochastic integrals. The Annals of Probability, 33(1), 177-193
  75. G. Peccati and C.A. Tudor (2004). Gaussian limits for vector-valued multiple stochastic integrals. Séminaire de Probabilités XXXVIII, 247-262
  76. G. Peccati (2004). Weak convergence to Ocone martingales: a remark. Electronic Communications in Probability 9, 172-174
  77. G. Peccati (2004). Anticipative stochastic integration based on time-space chaos. Stochastic Processes and Their Applications, 112(2), 331-355
  78. G. Peccati (2004). Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observations. The Annals of Probability 32 (3A), 1796-1829
  79. 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
  80. 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
  81. 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
  82. G. Peccati (2003). Explicit formulae for time-space Brownian chaos. Bernoulli, 9, 25-48
  83. G. Peccati (2001). On the convergence of multiple random integrals. Studia Sc. Mat. Hungarica, 37, 429-470
  84. G. Peccati (2001). A representation result for time-space Brownian chaos. Annales de l'Institut H. Poincaré (PR), 37, 607-625
  85. 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.