PAPERS 

Preprints

• 1. G. Peccati and M. Stecconi (2024). Nodal volumes as differentiable functionals of Gaussian fields.

  2. S. Favaro, B. Hanin, D. Marinucci, I. Nourdin and G. Peccati (2023). Quantitative CLTs in deep neural networks.

  3. F. Grotto and G. Peccati (2023). Nonlinear functionals of hyperbolic random waves: the Wiener chaos approach.

Published and accepted papers

1. M. Notarnicola, G. Peccati and A. Vidotto (2023+). Functional convergence of Berry's nodal length: approximate tightness and total disorder. To appear in: Journal of Statistical Physics

2. G. Peccati and N. Turchi (2023+). The discrepancy between min-max statistics of Gaussian and Gaussian-subordinated matrices. To appear in: Stochastic Processes and their Applications

3. G. Last, G. Peccati and D. Yogeshwaran (2023+). Phase transitions and noise sensitivity on the Poisson space via stopping sets and decision trees. To appear in: Random Structures & Algorithms

4. A. Jaramillo, I. Nourdin, D. Nualart and G. Peccati (2023+). Limit theorems for additive functionals of the fractional Brownian motion. To appear in: The Annals of Probability

5. M. Kasprzak and G. Peccati (2023+). Vector-valued statistics of binomial processes: Berry-Esseen bounds in the convex distance. To appear in: The Annals of Applied Probability

6. Ch. Döbler, M. Kasprzak and G. Peccati (2022). The multivariate functional de Jong CLT. Probability Theory and Related Fields, 184(1-2), 367-399

7. F. Grotto and G. Peccati (2022+). Infinitesimal invariance of completely random measures for 2D Euler equations. To appear in: Theory of Probability and its Applications

8. R. Lachièze-Rey, G. Peccati and X. Yang (2022). Quantitative two-scale stablization on the Poisson space. The Annals of Applied Probability, 32(4), 3085-3145

9. G. Dierickx, I. Nourdin, G. Peccati and M. Rossi (2022+). Small Scale CLTs for the Nodal Length of Monochromatic Waves. To appear in: Communications in Mathematical Physics

10. E. Azmoodeh, G. Peccati and X. Yang (2021). Malliavin-Stein method: a survey of recent developments. Modern Stochastics: Theory and Applications 8(2), 141-177

11. N. Gozlan, R. Herry and G. Peccati (2021). Transport inequalities for random point measures. Journal of Functional Analysis 281(9), paper 109141

12. I. Nourdin, G. Peccati and X. Yang (2022). Multivariate normal approximations on the Wiener space: new bounds in the convex distance. Journal of Theoretical Probability, 35(3), 2020-2037

13. Ch. Döbler, M. Kasprzak and G. Peccati (2022). Weak convergence of U-processes with size-dependent kernels. The Annals of Applied Probability, 32(1), 551-601

14. A. Jaramillo, I. Nourdin and G. Peccati (2021). Approximation of fractional local times: zero energy and derivatives. The Annals of Applied Probability 31(5), 2143-2191

15. F. Camia, A. Gandolfi, G. Peccati and T. R. Reddy (2021). Brownian loops, layering fields, and Gaussian multiplicative chaos. Communications in Mathematical Physics 381(3), 889-945

16. I. Nourdin, D. Nualart and G. Peccati (2021). The Breuer-Major Theorem in total variation: improved rates under minimal regularity. Stochastic Processes and their Applications 131, 1-20

17. G. Peccati and A. Vidotto (2020). Gaussian random measures generated by Berry's nodal sets. Journal of Statistical Physics 178(4), 996-1027

18. I. Nourdin, G. Peccati and X. Yang (2020). Restricted hypercontractivity on the Poisson space. Proceedings of the American Mathematical Society 148(8), 3617–3632

19. F. Dalmao, I. Nourdin, G. Peccati and M. Rossi (2019). Phase singularities in complex arithmetic random waves. Electronic Journal of Probability, Paper n. 71.

20. I. Nourdin, G. Peccati and X. Yang (2019). Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality. Electronic Communications in Probability, Paper n. 34.

21. I. Nourdin, G. Peccati and M. Rossi (2019). Nodal statistics of planar random waves. Communications in Mathematical Physics 369(1), 99-151.

22. M. Lotz, M. McCoy, I. Nourdin, G. Peccati, J. Tropp (2020). Concentration of the intrinsic volumes of a convex body. Geometric aspects of functional analysis. Vol. II, 139–167.

23. Ch. Döbler and G. Peccati (2019). Limit theorems for symmetric U-statistics using contractions. The Electronic Journal of Probability, paper n. 5.

24. I. Nourdin, G. Peccati and S. Seuret (2020). Sojourn time dimensions of fractional Brownian motion. Bernoulli 26(3), 1619-1634.

25. Ch. Döbler and G. Peccati (2018). Fourth moment theorems on the Poisson space: analytic statements via product formulae. Electronic Communications in Probability, paper n. 91, 12 pages.

26. G. Peccati and M. Rossi (2018). Quantitative limit theorems for local functionals of arithmetic random waves. In: Abel Symposium 2016 (Springer), 659-689.

27. Ch. Döbler and G. Peccati (2018). The fourth moment theorem on the Poisson space. The Annals of Probability 46(4), 1878-1916.

28. Ch. Döbler and G. Peccati (2018). The Gamma Stein equation and non central de Jong theorems. Bernoulli, 24(4B), 3384-3421.

29. M. Ledoux, I. Nourdin and G. Peccati (2016). A Stein deficit for the logarithmic Sobolev inequality. Science China Mathematics, 60(7), 1163-1180.

30. Ch. Döbler and G. Peccati (2016). Quantitative de Jong theorems in any dimension. Electronic Journal of Probability, 22, paper n.2, 35 pages.

31. G. Mijoule, G. Peccati and Y. Swan (2016). On the rate of convergence in de Finetti's representation theorem, ALEA, 13, 1165-1187.

32. S. Campese, I. Nourdin, G. Peccati and G. Poly (2016). Multivariate Gaussian approximation on Markov chaoses. Electronic Communications in Probability, 21, paper n. 48, 9 pages.

33. D. Marinucci, G. Peccati, M. Rossi and I. Wigman (2016). Non-universality of nodal length distribution for arithmetic random waves. Geometric and Functional Analysis, 26(3), 926-960.

34. R. Lachièze-Rey and G. Peccati (2017). New Kolmogorov bounds for functionals of binomial point processes. The Annals of Applied Probability, 27(4), 1992-20131.

35. I. Nourdin, G. Peccati, G. Poly and R. Simone (2016). Multidimensional limit theorems for homogeneous sums: a general transfer principle. ESAIM P&S, 20, 593-608.

36. E. Azmoodeh, G. Peccati and G. Poly (2016). The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds. ALEA, 13, 659-686.

37. L. Goldstein, I. Nourdin and G. Peccati (2017). Gaussian phase transitions and conic intrinsic volumes: Steining the Steiner formula. The Annals of Applied Probability, 27(1), 1-47.

38. I. Nourdin and G. Peccati (2017). Fourth moments and products: unified estimates. In: Convexity and concentration, 285–295, IMA Vol. Math. Appl., 161, Springer.

39. 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.

40. S. Bourguin, C. Durastanti, D. Marinucci and G. Peccati (2016). Gaussian approximations of non-linear statistics on the sphere. Journal of Mathematical Analysis and Applications, 436(2), 1121-1148

41. D. Malicet, I. Nourdin, G. Peccati and G. Poly (2016). Squared chaotic random variables: new moment inequalities with applications. Journal of Functional Analysis, 270(2), 649-670.

42. G. Last, G. Peccati and M. Schulte (2016). Normal approximations on the Poisson space: Mehler's formula, second order Poincaré inequalities and stabilization. Probability Theory and Related Fields, 165(3-4), 667-723.

43. I. Nourdin, D. Nualart and G. Peccati (2016). Strong asymptotic independence on Wiener chaos. Proceedings of the American Mathematical Society 144(2), 875-886.

44. I. Nourdin, G. Peccati, G. Poly and R. Simone (2016). Classical and free fourth moment theorems: universality and thresholds. Journal of Theoretical Probability, 29(2), 653-680.

45. 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.

46. M. Ledoux, I. Nourdin and G. Peccati (2015). Stein's method, logarithmic Sobolev and transport inequalities. Geometric and Functional Analysis 25, 256-306.

47. I. Nourdin and G. Peccati (2015). The optimal fourth moment theorem. Proceedings of the American Mathematical Society, 143(7), 3123-3133.

48. I. Nourdin, D. Nualart and G. Peccati (2016). Quantitative stable limit theorems on the Wiener space. The Annals of Probability, 44(1), 1-41.

49. 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.

50. I. Nourdin, G. Peccati and Y. Swan (2014). Integration by parts and representation of information functionals. Proceedings of the 2014 IEEE International Symposium on Information Theory (ISIT), Conference Location: Honolulu, HI. Pages 2217-2221

51. 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.

52. G. Peccati (2014). Quantitative CLTs on a Gaussian space: a survey of recent developments. ESAIM: PROCEEDINGS 44, pp. 61-78

53. 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)

54. I. Nourdin, G. Peccati and F. G. Viens (2014). Comparison inequalities on the Wiener space. Stochastic Processes and their Applications 124(4), 1566-1581.

55. I. Nourdin, G. Peccati and Y. Swan (2014). Entropy and the fourth moment phenomenon. Journal of Functional Analysis 266, 3170-3207.

56. G. Peccati and Ch. Thaele (2013). Gamma limits and U-statistics on the Poisson space. ALEA 10(1), 525-560.

57. 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.

58. 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.

59. 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.

60. G. Peccati and C. Zheng (2014). Universal Gaussian fluctuations on the discrete Poisson chaos. Bernoulli 20(2), 697-715.

61. 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.

62. I. Nourdin and G. Peccati (2013). Poisson approximations on the free Wigner chaos. The Annals of Probability 41(4), 2709-2723.

63. 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.

64. 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.

65. T. Kemp, I. Nourdin, G. Peccati and R. Speicher (2012). Wigner chaos and the fourth moment. The Annals of Probability 40(4), 1577-1635.

66. I. Nourdin, G. Peccati and M. Podolskij (2011). Quantitative Breuer-Major theorems. Stochastic Processes and their Applications 121, 793-812

67. 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)

68. G. Peccati and C. Zheng (2010). Multi-dimensional Gaussian fluctuations on the Poisson space. The Electronic Journal of Probability, 15; Paper 48: p. 1487-1527 (Electronic)

69. 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)

70. 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)

71. 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

72. D. Marinucci and G. Peccati (2010). Ergodicity and Gaussianity for Spherical Random Fields. Journal of Mathematical Physics 51, 043301

73. D. Marinucci and G. Peccati (2010). Representations of SO(3) and angular polyspectra. The Journal of Multivariate Analysis 101, 77-100

74. 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

75. I. Nourdin and G. Peccati (2010). Cumulants on the Wiener space. Journal of Functional Analysis 258, 3775-3791

76. 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

77. 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

78. 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

79. 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

80. D. Marinucci and G. Peccati (2010). Group representations and high-resolution central limit theorems for subordinated spherical random fields. Bernoulli 16(3), 798-824

81. P. De Blasi, G. Peccati and I. Pruenster (2010). On the asymptotic behaviour of random cumulative hazards. In: JSM Proceedings, 1063-1074

82. 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)

83. 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)

84. I. Nourdin and G. Peccati (2009). Non-central convergence of multiple integrals. The Annals of Probability 37(4), 1412–1426

85. S. Darses, I. Nourdin and G. Peccati (2009). Stochastic derivatives for Gaussian and shifted Gaussian processes.  Stochastics 81(1), 79-97

86. P. De Blasi, G. Peccati and I. Prünster (2009). Asymptotics for posterior hazards. The Annals of Statistics 37(4), 1906-1945

87. I. Nourdin and G. Peccati (2009). Stein's method on Wiener chaos. Probability Theory and Related Fields 145(1), 75-118

88. I. Nourdin and G. Peccati (2008). Weighted variations of iterated Brownian motion. The Electronic Journal of Probability 13, n. 43, 1229-1256 (Electronic)

89. G. Peccati and M.S. Taqqu (2008). Limit theorems for multiple stochastic integrals. ALEA 4, 393-413

90. G. Peccati and M.S. Taqqu (2008). Stable convergence of multiple Wiener-Itô integrals. The Journal of Theoretical Probability 21(3), 527-570

91. G. Peccati and M.S. Taqqu (2008). Central limit theorems for double Poisson integrals. Bernoulli 14(3), 791-821

92. O. El-Dakkak and G. Peccati (2008). Hoeffding decompositions and urn sequences. The Annals of Probability 36(6), 2280-2310

93. 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

94. G. Peccati and M. Yor (2008). Burkholder's submartingales from a stochastic calculus perspective. The Illinois Journal of Mathematics, 52(3), 815-824

95. 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

96. G. Peccati (2008). Multiple integral representation for functionals of Dirichlet processes. Bernoulli 14(1), 91-124

97. G. Peccati and C.A. Tudor (2007). Anticipating integrals and martingales on the Poisson space. Random Operators and Stochastic Equations 15, 327-352

98. G. Peccati (2007). Gaussian approximations of multiple integrals. Electronic Communications in Probability 12, 350-364 (Electronic)

99. 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)

100. G. Peccati, M. Thieullen and C.A. Tudor (2006). Martingale structure of Skorohod integral processes. The Annals of Probability, 34(3), 1217-1239

101. 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

102. 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

103. D. Nualart and G. Peccati (2005). Central limit theorems for sequences of multiple stochastic integrals. The Annals of Probability, 33(1), 177-193

104. G. Peccati and C.A. Tudor (2004). Gaussian limits for vector-valued multiple stochastic integrals. Séminaire de Probabilités XXXVIII, 247-262

105. G. Peccati (2004). Weak convergence to Ocone martingales: a remark. Electronic Communications in Probability 9, 172-174

106. G. Peccati (2004). Anticipative stochastic integration based on time-space chaos. Stochastic Processes and Their Applications, 112(2), 331-355

107. G. Peccati (2004). Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observations. The Annals of Probability 32 (3A), 1796-1829

108. 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

109. 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

110. 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

111. G. Peccati (2003). Explicit formulae for time-space Brownian chaos. Bernoulli, 9, 25-48

112. G. Peccati (2001). On the convergence of multiple random integrals. Studia Sc. Mat. Hungarica, 37, 429-470

113. G. Peccati (2001). A representation result for time-space Brownian chaos. Annales de l'Institut H. Poincaré (PR), 37, 607-625

114. G. Peccati (1998). Some results about Itô processe with jumps. Atti del XXIII Convegno AMASES.

Other papers

1. E. Azmoodeh and G. Peccati (2015). Optimal Berry-Esseen bounds on the Poisson space. 

2. G. Peccati (2011). The Chen-Stein method for Poisson functionals.

3. G. Peccati (2004). A time-space hedging theory. 

4. G. Peccati and M.S. Taqqu (2008). Moments, cumulants and diagram formulae for functionals of random measures.

5. I. Nourdin and G. Peccati (2009). Universal Gaussian fluctuations of non-Hermitian matrix ensembles.

6. From Wiener to time-space chaos, via conditioned Gaussian measures (2001), Preprint n. 648 du Laboratoire de Probabilités de l'Université Paris VI

7. 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.