Results 21-40 of 111.     Phase singularities in complex arithmetic random wavesDalmao, Federico; Nourdin, Ivan ; Peccati, Giovanni et alin Electronic Journal of Probability (2019), 24(71), 1-45Detailed reference viewed: 164 (11 UL) Multivariate stable approximation in Wasserstein distance by Stein's methodChen, Peng; Nourdin, Ivan ; Xu, Lihu et alE-print/Working paper (2019)Detailed reference viewed: 56 (0 UL) Non-integrable stable approximation by Stein's methodChen, Peng; Nourdin, Ivan ; Xu, Lihu et alE-print/Working paper (2019)Detailed reference viewed: 42 (0 UL) Asymptotic behaviour of large Gaussian correlated Wishart matricesNourdin, Ivan ; Zheng, Guangqu E-print/Working paper (2018)Detailed reference viewed: 49 (0 UL) Sojourn time dimensions of fractional Brownian motionNourdin, Ivan ; Peccati, Giovanni ; Seuret, StéphaneE-print/Working paper (2018)Detailed reference viewed: 91 (11 UL) Weak symmetric integrals with respect to the fractional Brownian motionBinotto, Giulia; Nourdin, Ivan ; Nualart, Davidin Annals of Probability (2018), 46(4), 2243-2267Detailed reference viewed: 219 (6 UL) Convergence of random oscillatory integrals in the presence of long-range dependence and application to homogenizationLechiheb, Atef; Nourdin, Ivan ; Zheng, Guangqu et alin Probability and Mathematical Statistics (2018), 38(2), 271-286Detailed reference viewed: 249 (12 UL) Exchangeable pairs on Wiener chaosNourdin, Ivan ; Zheng, Guangqu in High-Dimensional Probability VIII Proceedings (2017)Detailed reference viewed: 121 (5 UL) A Stein deficit for the logarithmic Sobolev inequalityLedoux, Michel; Nourdin, Ivan ; Peccati, Giovanni in Science China Mathematics (2017), 60Detailed reference viewed: 154 (4 UL) Gaussian Phase Transitions and Conic Intrinsic Volumes: Steining the Steiner FormulaGoldstein, Larry; Nourdin, Ivan ; Peccati, Giovanni in Annals of Applied Probability (2017), 27(1), 1-47Intrinsic 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 ▲]Detailed reference viewed: 189 (10 UL) Classical and free fourth moment theorems: universality and thresholdsNourdin, Ivan ; Peccati, Giovanni ; Poly, Guillaume et alin Journal of Theoretical Probability (2016), 29(2), 653-680Detailed reference viewed: 173 (11 UL) Convergence in law implies convergence in total variation for polynomials in independent Gaussian, Gamma or Beta random variablesPoly, Guillaume Joseph ; Nourdin, Ivan in Progress in Probability (2016), 71Detailed reference viewed: 139 (4 UL) Quantitative stable limit theorems on the Wiener spaceNourdin, Ivan ; Nualart, David; Peccati, Giovanni in Annals of Probability (2016), 44(1), 1-41Detailed reference viewed: 212 (12 UL) Asymptotic behaviour of the cross-variation of some integral long memory processesNourdin, Ivan ; Zintout, Rolain Probability and Mathematical Statistics (2016), 36(1), Detailed reference viewed: 69 (7 UL) Fisher information and the Fourth Moment TheoremNourdin, Ivan ; Nualart, Davidin Annales de l'Institut Henri Poincare (B) Probability & Statistics (2016), 52(2), 849-867Detailed reference viewed: 273 (13 UL) Strong asymptotic independence on Wiener chaosNourdin, Ivan ; Nualart, David; Peccati, Giovanni in Proceedings of the American Mathematical Society (2016), 144(2), 875-886Detailed reference viewed: 212 (15 UL) Multivariate Gaussian approxi- mations on Markov chaosesCampese, Simon ; Nourdin, Ivan ; Peccati, Giovanni et alin Electronic Communications in Probability (2016), 21Detailed reference viewed: 229 (8 UL) Squared chaotic random variables: new moment inequalities with applicationsMalicet, Dominique; Nourdin, Ivan ; Peccati, Giovanni et alin Journal of Functional Analysis (2016), 270(2), 649-670Detailed reference viewed: 218 (18 UL) Multidimensional limit theorems for homogeneous sums : a general transfer principleNourdin, Ivan ; Peccati, Giovanni ; Poly, Guillaume et alin ESAIM: Probability and Statistics (2016), 20Detailed reference viewed: 81 (2 UL) Convergence of random oscillatory integrals in the presence of long-range dependence and application to homogenizationLechiheb, Atef; Nourdin, Ivan ; Zheng, Guangqu et alin Probability and Mathematical Statistics (2016)Detailed reference viewed: 118 (6 UL)