References of "Peccati, Giovanni 50002826"
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See detailThe fourth moment theorem on the Poisson space
Döbler, Christian UL; Peccati, Giovanni UL

in Annals of Probability (in press)

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See detailThe Gamma Stein equation and non-central de Jong theorems
Döbler, Christian UL; Peccati, Giovanni UL

in Bernoulli (in press)

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See detailConcentration bounds for geometric Poisson functionals: logarithmic Sobolev inequalities revisited
Peccati, Giovanni UL; Bachmann, Sascha

in Electronic Journal of Probability (in press)

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See detailLimit theorems for symmetric U-statistics using contractions
Döbler, Christian UL; Peccati, Giovanni UL

E-print/Working paper (2018)

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See detailSojourn time dimensions of fractional Brownian motion
Nourdin, Ivan UL; Peccati, Giovanni UL; Seuret, Stéphane

E-print/Working paper (2018)

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See detailNew Kolmogorov bounds for functionals of binomial point processes
Peccati, Giovanni UL; Lachièze-Rey, Raphael

in Annals of Applied Probability (2017), 27(4), 1992-20131

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See detailQuantitative de Jong theorems in any dimension
Döbler, Christian UL; Peccati, Giovanni UL

in Electronic Journal of Probability (2017), 22

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See detailNodal Statistics of Planar Random Waves
Nourdin, Ivan UL; Peccati, Giovanni UL; Rossi, Maurizia UL

E-print/Working paper (2017)

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See detailGaussian Phase Transitions and Conic Intrinsic Volumes: Steining the Steiner Formula
Goldstein, Larry; Nourdin, Ivan UL; Peccati, Giovanni UL

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

Intrinsic volumes of convex sets are natural geometric quantities that also play important roles in applications, such as linear inverse problems with convex constraints, and constrained statistical ... [more ▼]

Intrinsic volumes of convex sets are natural geometric quantities that also play important roles in applications, such as linear inverse problems with convex constraints, and constrained statistical inference. It is a well-known fact that, given a closed convex cone $C\subset \mathbb{R}^d$, its conic intrinsic volumes determine a probability measure on the finite set $\{0,1,...d\}$, customarily denoted by $\mathcal{L}(V_C)$. The aim of the present paper is to provide a Berry-Esseen bound for the normal approximation of ${\cal L}(V_C)$, implying a general quantitative central limit theorem (CLT) for sequences of (correctly normalised) discrete probability measures of the type $\mathcal{L}(V_{C_n})$, $n\geq 1$. This bound shows that, in the high-dimensional limit, most conic intrinsic volumes encountered in applications can be approximated by a suitable Gaussian distribution. Our approach is based on a variety of techniques, namely: (1) Steiner formulae for closed convex cones, (2) Stein's method and second order Poincar\'e inequality, (3) concentration estimates, and (4) Fourier analysis. Our results explicitly connect the sharp phase transitions, observed in many regularised linear inverse problems with convex constraints, with the asymptotic Gaussian fluctuations of the intrinsic volumes of the associated descent cones. In particular, our findings complete and further illuminate the recent breakthrough discoveries by Amelunxen, Lotz, McCoy and Tropp (2014) and McCoy and Tropp (2014) about the concentration of conic intrinsic volumes and its connection with threshold phenomena. As an additional outgrowth of our work we develop total variation bounds for normal approximations of the lengths of projections of Gaussian vectors on closed convex sets. [less ▲]

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See detailA Stein deficit for the logarithmic Sobolev inequality
Ledoux, Michel; Nourdin, Ivan UL; Peccati, Giovanni UL

in Science China Mathematics (2017), 60

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See detailPhase singularities in complex arithmetic random waves
Dalmao, Federico; Nourdin, Ivan UL; Peccati, Giovanni UL et al

E-print/Working paper (2016)

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See detailClassical and free fourth moment theorems: universality and thresholds
Nourdin, Ivan UL; Peccati, Giovanni UL; Poly, Guillaume et al

in Journal of Theoretical Probability (2016), 29(2), 653-680

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See detailThe law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds
Azmoodeh, Ehsan UL; Peccati, Giovanni UL; Poly, Guillaume

in ALEA: Latin American Journal of Probability and Mathematical Statistics (2016), 13

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See detailGaussian approximations of nonlinear statistis on the sphere
Bourguin, Solesne; Durastanti, Claudio; Marinucci, Domenico et al

in Journal of Mathematical Analysis and Applications (2016), 436(2), 1121-1148

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See detailQuantitative stable limit theorems on the Wiener space
Nourdin, Ivan UL; Nualart, David; Peccati, Giovanni UL

in Annals of Probability (2016), 44(1), 1-41

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See detailNormal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization
Last, Guenter; Peccati, Giovanni UL; Schulte, Matthias

in Probability Theory & Related Fields (2016), 165(3), 667-723

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See detailStrong asymptotic independence on Wiener chaos
Nourdin, Ivan UL; Nualart, David; Peccati, Giovanni UL

in Proceedings of the American Mathematical Society (2016), 144(2), 875-886

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See detailMultidimensional limit theorems for homogeneous sums : a general transfer principle
Nourdin, Ivan UL; Peccati, Giovanni UL; Poly, Guillaume et al

in ESAIM: Probability and Statistics = Probabilité et statistique : P & S (2016), 20

Detailed reference viewed: 41 (1 UL)