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Continuous Breuer-Major theorem: tightness and non-stationarity Campese, Simon ; Nourdin, Ivan ; in Annals of Probability (in press) Detailed reference viewed: 22 (2 UL)The functional Breuer-Major theorem Nourdin, Ivan ; in Probability Theory and Related Fields (in press) Detailed reference viewed: 59 (7 UL)Statistical inference for Vasicek-type model driven by Hermite processes Nourdin, Ivan ; Tran, Thi Thanh Diu in Stochastic Processes and Their Applications (in press) Detailed reference viewed: 133 (4 UL)Phase singularities in complex arithmetic random waves ; Nourdin, Ivan ; Peccati, Giovanni et al in Electronic Journal of Probability (2019), 24(71), 1-45 Detailed reference viewed: 81 (4 UL)Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality Nourdin, Ivan ; Peccati, Giovanni ; Yang, Xiaochuan in Electronic Communications in Probability (2019), 24(34), 1-12 Detailed reference viewed: 30 (1 UL)Almost sure limit theorems on Wiener chaos: the non-central case ; Nourdin, Ivan in Electronic Communications in Probability (2019), 24(9), 1-12 Detailed reference viewed: 52 (3 UL)Nodal Statistics of Planar Random Waves Nourdin, Ivan ; Peccati, Giovanni ; in Communications in Mathematical Physics (2019), 369(1), 99-151 Detailed reference viewed: 94 (10 UL)Sojourn time dimensions of fractional Brownian motion Nourdin, Ivan ; Peccati, Giovanni ; E-print/Working paper (2018) Detailed reference viewed: 38 (5 UL)Stein's method for asymmetric alpha-stable distributions, with application to the stable CLT ; Nourdin, Ivan ; E-print/Working paper (2018) Detailed reference viewed: 39 (1 UL)Asymptotic behaviour of large Gaussian correlated Wishart matrices Nourdin, Ivan ; Zheng, Guangqu E-print/Working paper (2018) Detailed reference viewed: 10 (0 UL)Weak symmetric integrals with respect to the fractional Brownian motion ; Nourdin, Ivan ; in Annals of Probability (2018), 46(4), 2243-2267 Detailed reference viewed: 147 (2 UL)Concentration of the Intrinsic Volumes of a Convex Body ; ; Nourdin, Ivan et al E-print/Working paper (2018) Detailed reference viewed: 29 (0 UL)Convergence of random oscillatory integrals in the presence of long-range dependence and application to homogenization ; Nourdin, Ivan ; Zheng, Guangqu et al in Probability and Mathematical Statistics (2018), 38(2), 271-286 Detailed reference viewed: 196 (12 UL)Exchangeable pairs on Wiener chaos Nourdin, Ivan ; Zheng, Guangqu in High-Dimensional Probability VIII Proceedings (2017) Detailed reference viewed: 69 (5 UL)Freeness characterisations on free chaos spaces Bourguin, Solesne ; Nourdin, Ivan E-print/Working paper (2017) Detailed reference viewed: 74 (1 UL)Gaussian Phase Transitions and Conic Intrinsic Volumes: Steining the Steiner Formula ; Nourdin, Ivan ; Peccati, Giovanni 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 ▲] Detailed reference viewed: 120 (5 UL)A Stein deficit for the logarithmic Sobolev inequality ; Nourdin, Ivan ; Peccati, Giovanni in Science China Mathematics (2017), 60 Detailed reference viewed: 81 (3 UL)Classical and free fourth moment theorems: universality and thresholds Nourdin, Ivan ; Peccati, Giovanni ; et al in Journal of Theoretical Probability (2016), 29(2), 653-680 Detailed reference viewed: 109 (8 UL)Convergence in law implies convergence in total variation for polynomials in independent Gaussian, Gamma or Beta random variables Poly, Guillaume Joseph ; Nourdin, Ivan in Progress in Probability (2016), 71 Detailed reference viewed: 76 (4 UL)Quantitative stable limit theorems on the Wiener space Nourdin, Ivan ; ; Peccati, Giovanni in Annals of Probability (2016), 44(1), 1-41 Detailed reference viewed: 137 (11 UL) |
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