References of "Nourdin, Ivan 50002770"
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See detailStatistical inference for Vasicek-type model driven by Hermite processes
Nourdin, Ivan UL; Tran, Thi Thanh Diu UL

in Stochastic Processes and Their Applications (in press)

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

in Communications in Mathematical Physics (in press)

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See detailWeak symmetric integrals with respect to the fractional Brownian motion
Binotto, Giulia; Nourdin, Ivan UL; Nualart, David

in Annals of Probability (2018), 46(4), 2243-2267

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See detailConvergence of random oscillatory integrals in the presence of long-range dependence and application to homogenization
Lechiheb, Atef; Nourdin, Ivan UL; Zheng, Guangqu UL et al

in Probability and Mathematical Statistics (2018), 38(2), 271-286

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See detailAlmost sure limit theorems on Wiener chaos: the non-central case
Azmoodeh, Ehsan; Nourdin, Ivan UL

E-print/Working paper (2018)

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See detailThe functional Breuer-Major theorem
Nourdin, Ivan UL; Nualart, David

E-print/Working paper (2018)

Detailed reference viewed: 44 (0 UL)
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See detailStein's method for asymmetric alpha-stable distributions, with application to the stable CLT
Chen, Peng; Nourdin, Ivan UL; Xu, Lihu

E-print/Working paper (2018)

Detailed reference viewed: 37 (1 UL)
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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)

Detailed reference viewed: 37 (5 UL)
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See detailContinuous Breuer-Major theorem: tightness and non-stationarity
Campese, Simon UL; Nourdin, Ivan UL; Nualart, David

E-print/Working paper (2018)

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See detailConcentration of the Intrinsic Volumes of a Convex Body
Lotz, Martin; McCoy, Michael B.; Nourdin, Ivan UL et al

E-print/Working paper (2018)

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See detailAsymptotic behaviour of large Gaussian correlated Wishart matrices
Nourdin, Ivan UL; Zheng, Guangqu UL

E-print/Working paper (2018)

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See detailExchangeable pairs on Wiener chaos
Nourdin, Ivan UL; Zheng, Guangqu UL

in High-Dimensional Probability VIII Proceedings (2017)

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See detailFreeness characterisations on free chaos spaces
Bourguin, Solesne UL; Nourdin, Ivan 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 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 detailMultivariate Gaussian approxi- mations on Markov chaoses
Campese, Simon UL; Nourdin, Ivan UL; Peccati, Giovanni UL et al

in Electronic Communications in Probability (2016), 21

Detailed reference viewed: 150 (7 UL)