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Prof. Dr. Giovanni Peccati
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| Faculty or Centre | Faculty of Science, Technology and Medicine | ||||||
| Department | Department of Mathematics | ||||||
| Postal Address |
Université du Luxembourg Maison du Nombre 6, Avenue de la Fonte L-4364 Esch-sur-Alzette |
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| Campus Office | MNO, E05 0515-100 | ||||||
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| Telephone | (+352) 46 66 44 5772 | ||||||
External homepage: http://sites.google.com/site/giovannipeccati/home
Last updated on: Monday, 25 October 2021
In press
Limit theorems for additive functionals of the fractional Brownian motion; ; ;
in Annals of Probability (in press)
Vector-valued statistics of binomial processes: Berry-Esseen bounds in the convex distance;
in Annals of Applied Probability (in press)
Phase transitions and noise sensitivity on the Poisson space via stopping sets and decision trees; ;
in Random Structures and Algorithms (in press)
2023
Small Scale CLTs for the Nodal Length of Monochromatic Waves; ; ;
in Communications in Mathematical Physics (2023), 397(1), 1-36
The discrepancy between min-max statistics of Gaussian and Gaussian-subordinated matrices;
in Stochastic Processes and Their Applications (2023), 158
2022
Functional Convergence of U-processes with Size-Dependent Kernels; ;
in Annals of Applied Probability (2022), 32(1), 551-601
The multivariate functional de Jong CLT; ;
in Probability Theory and Related Fields (2022), 184(1), 367-399
Quantitative two-scale stabilization on the Poisson space; ;
in Annals of Applied Probability (2022)
Multivariate normal approximation on the Wiener space: new bounds in the convex distance; ;
in Journal of Theoretical Probability (2022)
2021
Malliavin-Stein method: a survey of some recent developments; ;
in Modern Stochastics: Theory and Applications (2021), 8(2), 141-177
Brownian Loops, Layering Fields and Imaginary Gaussian Multiplicative Chaos; ; ;
in Communications in Mathematical Physics (2021), 381(3), 889-945
Transport inequalities for random point measures; ;
in Journal of Functional Analysis (2021), 281(9),
Approximation of Fractional Local Times: Zero Energy and Derivatives; ;
in Annals of Applied Probability (2021), In press
The Breuer-Major Theorem in total variation: improved rates under minimal regularity; ;
in Stochastic Processes and Their Applications (2021), 131
2020
Restricted hypercontractivity on the Poisson space; ;
in Proceedings of the American Mathematical Society (2020), 148
Gaussian Random Measures Generated by Berry's Nodal Sets;
in Journal of Statistical Physics (2020), 178(4), 996-1027
2019
Phase singularities in complex arithmetic random waves; ; ;
in Electronic Journal of Probability (2019), 24(71), 1-45
Quantitative limit theorems for symmetric U-statistics using contractions;
in Electronic Journal of Probability (2019), 24
Quantitative CLTs for symmetric U-statistics using contractions;
in Electronic Journal of Probability (2019), 24
Nodal Statistics of Planar Random Waves; ;
in Communications in Mathematical Physics (2019), 369(1), 99-151
Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality; ;
in Electronic Communications in Probability (2019), 24(34), 1-12
2018
Fourth moment theorems on the Poisson space: analytic statements via product formulae;
in Electronic Communications in Probability (2018), 23
Concentration of the Intrinsic Volumes of a Convex Body; ; ; ;
in Geometric Aspects of Functional Analysis – Israel Seminar (GAFA) 2017-2019 (2018)
Quantitative limit theorems for local functionals of arithmetic random waves;
in Celledoni, Elena (Ed.) Computation and combinatorics in dynamics, stochastics and control. (2018)
2017
Gaussian Phase Transitions and Conic Intrinsic Volumes: Steining the Steiner Formula; ;
in Annals of Applied Probability (2017), 27(1), 1-47
New Kolmogorov bounds for functionals of binomial point processes;
in Annals of Applied Probability (2017), 27(4), 1992-20131
2016
The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds; ;
in ALEA: Latin American Journal of Probability and Mathematical Statistics (2016), 13
Gaussian approximations of nonlinear statistis on the sphere; ; ;
in Journal of Mathematical Analysis and Applications (2016), 436(2), 1121-1148
Multivariate Gaussian approxi- mations on Markov chaoses; ; ;
in Electronic Communications in Probability (2016), 21
Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization; ;
in Probability Theory and Related Fields (2016), 165(3), 667-723
Squared chaotic random variables: new moment inequalities with applications; ; ;
in Journal of Functional Analysis (2016), 270(2), 649-670
Non-universality of nodal length distribution for arithmetic random waves; ; ;
in Geometric and Functional Analysis (2016), 26(3), 926-960
Quantitative stable limit theorems on the Wiener space; ;
in Annals of Probability (2016), 44(1), 1-41
Strong asymptotic independence on Wiener chaos; ;
in Proceedings of the American Mathematical Society (2016), 144(2), 875-886
Classical and free fourth moment theorems: universality and thresholds; ; ;
in Journal of Theoretical Probability (2016), 29(2), 653-680
Multidimensional limit theorems for homogeneous sums : a general transfer principle; ; ;
in ESAIM: Probability and Statistics (2016), 20
Concentration bounds for geometric Poisson functionals: logarithmic Sobolev inequalities revisited;
in Electronic Journal of Probability (2016), 6(44),
Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry;
Book published by Springer (2016)
2015
Convergence towards linear combinations of chi-squared random variables: a Malliavin-based approach.; ;
in Séminaire de Probabilités (2015)
Stein's method, logarithmic Sobolev and transport inequalities; ;
in Geometric and Functional Analysis (2015), 25
The optimal fourth moment theorem;
in Proceedings of the American Mathematical Society (2015), 143(7), 3123-3133
2014
Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering;
in Electronic Journal of Probability (2014), 19(Paper 66),
Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle;
in Journal of Functional Analysis (2014), 267(4),
Normal approximations for wavelet coefficients on spherical Poisson fields; ;
in Journal of Mathematical Analysis and Applications (2014), 409(1), 212--227
Exchangeable Hoeffding decompositions over finite sets: a characterization and counterexamples; ;
in Journal of Multivariate Analysis (2014), 131
Entropy and the fourth moment phenomenon; ;
in Journal of Functional Analysis (2014), 266(5), 3170-3207
Integration by parts and representation of information functionals; ;
in Abstract book of 2014 IEEE International Symposium on Information Theory (ISIT) (2014)
Comparison inequalities on the Wiener space; ;
in Stochastic Processes and Their Applications (2014), 124(4), 1566-1581
Quantitative CLTs on a Gaussian space: a survey of recent developmentsin ESAIM: Proceedings and Surveys (2014), 44
2013
Fine Gaussian fluctuations on the Poisson space II: Rescaled kernels, marked processes and geometric $U$-statistics;
in Stochastic Processes and Their Applications (2013), 123(12), 4186--4218
Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs;
in Electronic Journal of Probability (2013), 18
Mean-square continuity on homogeneous spaces of compact groups;
in Electronic Communications in Probability (2013), 18
Multidimensional semicircular limits on the free Wigner chaos; ;
in The Ascona Proceedings, 2011 (2013)
Gamma limits and $U$-statistics on the Poisson space;
in Latin American Journal of Probability and Mathematical Statistics (2013), 10(1), 525--560
2012
Optimal Berry-Esseen rates on the Wiener space: the barrier of third and fourth cumulants; ; ;
in Latin American Journal of Probability and Mathematical Statistics (2012), 9(2), 473--500
2011
Quantitative Breuer-Major theorems; ;
in Stochastic Processes and Their Applications (2011), 121(4), 793--812
Hoeffding spaces and Specht modules;
in ESAIM: Probability and Statistics (2011), 15(In honor of Marc Yor, suppl.), 58--68
2010
Representations of SO(3) and angular polyspectra;
in Journal of Multivariate Analysis (2010), 101(1), 77--100
Group representations and high-resolution central limit theorems for subordinated spherical random fields;
in Bernoulli (2010), 16(3), 798--824
Ergodicity and Gaussianity for spherical random fields;
in Journal of Mathematical Physics (2010), 51(4), 04330123
Stein's method meets Malliavin calculus: a short survey with new estimates;
in Recent development in stochastic dynamics and stochastic analysis (2010)
Universal Gaussian fluctuations of non-Hermitian matrix ensembles: from weak convergence to almost sure CLTs;
in Latin American Journal of Probability and Mathematical Statistics (2010), 7
Multivariate normal approximation using Stein's method and Malliavin calculus; ;
in Annales de l'Institut Henri Poincare (B) Probability & Statistics (2010), 46(1), 45--58
Stein's method and stochastic analysis of Rademacher functionals; ;
in Electronic Journal of Probability (2010), 15
Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos; ;
in Annals of Probability (2010), 38(5), 1947--1985
Stein's method and normal approximation of Poisson functionals; ; ;
in Annals of Probability (2010), 38(2), 443--478
Multi-dimensional Gaussian fluctuations on the Poisson space;
in Electronic Journal of Probability (2010), 15
2009
Exact confidence intervals for the Hurst parameter of a fractional Brownian motion; ;
in Electronic Journal of Statistics (2009), 3
Differentiating $\sigma$-fields for Gaussian and shifted Gaussian processes; ;
in Stochastics: an International Journal of Probablitiy and Stochastic Processes (2009), 81(1), 79--97
Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields;
in Annals of Probability (2009), 37(6), 2231--2261
Second order Poincaré inequalities and CLTs on Wiener space; ;
in Journal of Functional Analysis (2009), 257(2), 593--609
Decompositions of stochastic processes based on irreducible group representations;
in Theory of Probability & Its Applications (2009), 54(2), 304--336
2008
High-frequency asymptotics for subordinated stationary fields on an abelian compact group;
in Stochastic Processes and Their Applications (2008), 118(4), 585--613
Weighted power variations of iterated Brownian motion;
in Electronic Journal of Probability (2008), 13
Multiple integral representation for functionals of Dirichlet processesin Bernoulli (2008), 14(1), 91--124
Linear and quadratic functionals of random hazard rates: an asymptotic analysis;
in Annals of Applied Probability (2008), 18(5), 1910--1943
Limit theorems for multiple stochastic integrals;
in Latin American Journal of Probability and Mathematical Statistics (2008), 4
Stable convergence of multiple Wiener-It\^o integrals;
in Journal of Theoretical Probability (2008), 21(3), 527--570
Burkholder's submartingales from a stochastic calculus perspective;
in Illinois Journal of Mathematics (2008), 52(3), 815--824
2007
Stable convergence of generalized $L^2$ stochastic integrals and the principle of conditioning;
in Electronic Journal of Probability (2007), 12
Anticipating integrals and martingales on the Poisson space;
in Random Operators and Stochastic Equations (2007), 15(4), 327--352
2006
On quadratic functionals of the Brownian sheet and related processes; ;
in Stochastic Processes and Their Applications (2006), 116(3), 493--538
Martingale structure of Skorohod integral processes; ;
in Annals of Probability (2006), 34(3), 1217--1239
Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections;
in Approximation and probability (2006)
2005
Central limit theorems for sequences of multiple stochastic integrals;
in Annals of Probability (2005), 33(1), 177--193
Gaussian limits for vector-valued multiple stochastic integrals;
in Séminaire de Probabilités XXXVIII (2005)
2004
Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observationsin Annals of Probability (2004), 32(3A), 1796--1829
Weak convergence to Ocone martingales: a remarkin Electronic Communications in Probability (2004), 9
Anticipative stochastic integration based on time-space chaosin Stochastic Processes and Their Applications (2004), 112(2), 331--355
Four limit theorems for quadratic functionals of Brownian motion and Brownian bridge;
in Asymptotic methods in stochastics (2004)
Hardy's inequality in $L^2([0,1])$ and principal values of Brownian local times;
in Asymptotic methods in stochastics (2004)
2003
Hoeffding decompositions for exchangeable sequences and chaotic representation of functionals of Dirichlet processesin Comptes Rendus. Mathématique (2003), 336(10), 845--850
2001
A representation result for time-space Brownian chaosin Annales de l'Institut Henri Poincare (B) Probability & Statistics (2001), 37(5), 607--625
On the convergence of multiple random integralsin Studia Scientiarum Mathematicarum Hungarica (2001), 37(3-4), 429--470
