# Giovanni Peccati

### Full professor in Stochastic analysis and financial mathematics

Sujets de recherche Probability Theory and Mathematical Finance
Faculté ou Centre Faculty of Science, Technology and Communication
Unité de recherche RU Mathematics
Maison du Nombre
6, Avenue de la Fonte
L-4364 Esch-sur-Alzette
Bureau sur le campus MNO, E05 0515-100
E-mail
Téléphone (+352) 46 66 44 5772
Fax (+352) 46 66 44 35772

Last updated on: lundi 22 octobre 2018

# Sous presse

The fourth moment theorem on the Poisson space
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in Annals of Probability (in press)

The Gamma Stein equation and non-central de Jong theorems
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in Bernoulli (in press)

Concentration bounds for geometric Poisson functionals: logarithmic Sobolev inequalities revisited
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in Electronic Journal of Probability (in press)

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# 2019

Phase singularities in complex arithmetic random waves
; ; ;

in Electronic Journal of Probability (2019), 24(71), 1-45

Quantitative CLTs for symmetric U-statistics using contractions
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in Electronic Journal of Probability (2019)

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
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in Electronic Communications in Probability (2019), 24(34), 1-12

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# 2018

Limit theorems for symmetric U-statistics using contractions
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E-print/Working paper (2018)

Fourth moment theorems on the Poisson space: analytic statements via product formulae
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in Electronic Communications in Probability (2018), 23

Concentration of the Intrinsic Volumes of a Convex Body
; ; ; ;

E-print/Working paper (2018)

Sojourn time dimensions of fractional Brownian motion
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E-print/Working paper (2018)

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# 2017

Quantitative de Jong theorems in any dimension
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in Electronic Journal of Probability (2017), 22

Gaussian Phase Transitions and Conic Intrinsic Volumes: Steining the Steiner Formula
; ;

in Annals of Applied Probability (2017), 27(1), 1-47

A Stein deficit for the logarithmic Sobolev inequality
; ;

in Science China Mathematics (2017), 60

New Kolmogorov bounds for functionals of binomial point processes
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in Annals of Applied Probability (2017), 27(4), 1992-20131

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# 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 & 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 & 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 = Probabilité et statistique : P & S (2016), 20

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# 2015

Convergence towards linear combinations of chi-squared random variables: a Malliavin-based approach.
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in Séminaire de Probabilités XLVII (2015)

Stein's method, logarithmic Sobolev and transport inequalities
; ;

in Geometric & Functional Analysis (2015), 25

The optimal fourth moment theorem
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in Proceedings of the American Mathematical Society (2015), 143(7), 3123-3133

Optimal Berry-Esseen bounds on the Poisson space.
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E-print/Working paper (2015)

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# 2014

Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering
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in Electronic Journal of Probability (2014), 19(Paper 66),

Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle
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in Journal of Functional Analysis (2014), 267(4),

Normal approximations for wavelet coefficients on spherical Poisson fields
; ;

in Journal of Mathematical Analysis & 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 & Their Applications (2014), 124(4), 1566-1581

Quantitative CLTs on a Gaussian space: a survey of recent developments

in ESAIM: Proceedings and Surveys (2014), 44

Universal Gaussian fluctuations on the discrete Poisson chaos
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in Bernoulli (2014), 20(2), 697-715

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# 2013

Fine Gaussian fluctuations on the Poisson space II: Rescaled kernels, marked processes and geometric $U$-statistics
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in Stochastic Processes & Their Applications (2013), 123(12), 4186--4218

Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs
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in Electronic Journal of Probability (2013), 18

Mean-square continuity on homogeneous spaces of compact groups
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in Electronic Communications in Probability (2013), 18

Poisson approximations on the free Wigner chaos
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in Annals of Probability (2013), 41(4), 2709--2723

Multidimensional semicircular limits on the free Wigner chaos
; ;

in The Ascona Proceedings, 2011 (2013)

Gamma limits and $U$-statistics on the Poisson space
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in Latin American Journal of Probability and Mathematical Statistics (2013), 10(1), 525--560

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# 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

Wigner chaos and the fourth moment
; ; ;

in Annals of Probability (2012), 40(4), 1577--1635

Normal approximations with Malliavin calculus
;

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# 2011

Random fields on the sphere
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Quantitative Breuer-Major theorems
; ;

in Stochastic Processes & Their Applications (2011), 121(4), 793--812

The Chen-Stein method for Poisson functionals

E-print/Working paper (2011)

Hoeffding spaces and Specht modules
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in ESAIM Probab. Stat. (2011), 15(In honor of Marc Yor, suppl.), 58--68

Wiener chaos: moments, cumulants and diagrams
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# 2010

Representations of SO(3) and angular polyspectra
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in Journal of Multivariate Analysis (2010), 101(1), 77--100

Group representations and high-resolution central limit theorems for subordinated spherical random fields
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in Bernoulli (2010), 16(3), 798--824

Ergodicity and Gaussianity for spherical random fields
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in Journal of Mathematical Physics (2010), 51(4), 04330123

Stein's method meets Malliavin calculus: a short survey with new estimates
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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
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in Latin American Journal of Probability and Mathematical Statistics (2010), 7

Cumulants on the Wiener space
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in Journal of Functional Analysis (2010), 258(11), 3775--3791

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
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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
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in Electronic Journal of Probability (2010), 15

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# 2009

Exact confidence intervals for the Hurst parameter of a fractional Brownian motion
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in Electronic Journal of Statistics (2009), 3

Differentiating $\sigma$-fields for Gaussian and shifted Gaussian processes
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in Stochastics (2009), 81(1), 79--97

Asymptotics for posterior hazards
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in Annals of Statistics (2009), 37(4), 1906--1945

Stein's method on Wiener chaos
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in Probab. Theory Related Fields (2009), 145(1-2), 75--118

Noncentral convergence of multiple integrals
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in Annals of Probability (2009), 37(4), 1412--1426

Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields
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in Annals of Probability (2009), 37(6), 2231--2261

Second order Poincaré inequalities and CLTs on Wiener space
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in Journal of Functional Analysis (2009), 257(2), 593--609

Decompositions of stochastic processes based on irreducible group representations
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in Theory of Probability & Its Applications (2009), 54(2), 304--336

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# 2008

Hoeffding decompositions and urn sequences
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in Annals of Probability (2008), 36(6), 2280--2310

High-frequency asymptotics for subordinated stationary fields on an abelian compact group
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in Stochastic Processes & Their Applications (2008), 118(4), 585--613

Weighted power variations of iterated Brownian motion
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in Electronic Journal of Probability (2008), 13

Multiple integral representation for functionals of Dirichlet processes

in Bernoulli (2008), 14(1), 91--124

Linear and quadratic functionals of random hazard rates: an asymptotic analysis
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in Annals of Applied Probability (2008), 18(5), 1910--1943

Central limit theorems for double Poisson integrals
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in Bernoulli (2008), 14(3), 791--821

Limit theorems for multiple stochastic integrals
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in Latin American Journal of Probability and Mathematical Statistics (2008), 4

Stable convergence of multiple Wiener-It\^o integrals
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in Journal of Theoretical Probability (2008), 21(3), 527--570

Burkholder's submartingales from a stochastic calculus perspective
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in Illinois Journal of Mathematics (2008), 52(3), 815--824

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# 2007

Gaussian approximations of multiple integrals

in Electronic Communications in Probability (2007), 12

Stable convergence of generalized $L^2$ stochastic integrals and the principle of conditioning
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in Electronic Journal of Probability (2007), 12

Anticipating integrals and martingales on the Poisson space
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in Random Oper. Stoch. Equ. (2007), 15(4), 327--352

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# 2006

On quadratic functionals of the Brownian sheet and related processes
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in Stochastic Processes & Their Applications (2006), 116(3), 493--538

Martingale structure of Skorohod integral processes
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in Annals of Probability (2006), 34(3), 1217--1239

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# 2005

Central limit theorems for sequences of multiple stochastic integrals
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in Annals of Probability (2005), 33(1), 177--193

Gaussian limits for vector-valued multiple stochastic integrals
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in Séminaire de Probabilités XXXVIII (2005)

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# 2004

Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observations

in Annals of Probability (2004), 32(3A), 1796--1829

Weak convergence to Ocone martingales: a remark

in Electronic Communications in Probability (2004), 9

Anticipative stochastic integration based on time-space chaos

in Stochastic Processes & Their Applications (2004), 112(2), 331--355

Four limit theorems for quadratic functionals of Brownian motion and Brownian bridge
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in Asymptotic methods in stochastics (2004)

Hardy's inequality in $L^2([0,1])$ and principal values of Brownian local times
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in Asymptotic methods in stochastics (2004)

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# 2003

Explicit formulae for time-space Brownian chaos

in Bernoulli (2003), 9(1), 25--48

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# 2001

A representation result for time-space Brownian chaos

in Annales de l'Institut Henri Poincare (B) Probability & Statistics (2001), 37(5), 607--625

On the convergence of multiple random integrals

in Studia Scientiarum Mathematicarum Hungarica (2001), 37(3-4), 429--470

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# Undated

The Breuer-Major Theorem in total variation: improved rates under minimal regularity
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E-print/Working paper (n.d.)

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