Entropy and the fourth moment phenomenon
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Publication:2253134
DOI10.1016/j.jfa.2013.09.017zbMath1292.94010arXiv1312.5276OpenAlexW2164057361MaRDI QIDQ2253134
Giovanni Peccati, Ivan Nourdin, Yvik Swan
Publication date: 25 July 2014
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1312.5276
relative entropyFisher informationcentral limit theoremGaussian fieldsfourth moment theoremCarbery-Wright inequalityStein factorsde Bruijn's formula
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Generalization of the Nualart-Peccati criterion ⋮ Non-integrable stable approximation by Stein's method ⋮ Fisher information and the fourth moment theorem ⋮ Classical and free fourth moment theorems: universality and thresholds ⋮ Quantitative clts on a gaussian space: a survey of recent developments ⋮ On Stein's method for multivariate self-decomposable laws with finite first moment ⋮ A stroll along the gamma ⋮ Stein's method for functions of multivariate normal random variables ⋮ Multidimensional limit theorems for homogeneous sums: A survey and a general transfer principle ⋮ Some inequalities on Riemannian manifolds linking entropy, Fisher information, Stein discrepancy and Wasserstein distance ⋮ From \(p\)-Wasserstein bounds to moderate deviations ⋮ Normal Approximation on a Finite Wiener Chaos ⋮ Higher-order Stein kernels for Gaussian approximation ⋮ Approximation of stable law in Wasserstein-1 distance by Stein's method ⋮ Statistical analysis of some evolution equations driven by space-only noise ⋮ Malliavin-Stein method: a survey of some recent developments ⋮ High-dimensional central limit theorems by Stein's method ⋮ Recent advances in various fields of numerical probability ⋮ Multivariate second order Poincaré inequalities for Poisson functionals ⋮ Some new Stein operators for product distributions ⋮ Cumulants on Wiener chaos: moderate deviations and the fourth moment theorem ⋮ An algebra of Stein operators ⋮ Existence of Stein kernels under a spectral gap, and discrepancy bounds ⋮ Multivariate normal approximation on the Wiener space: new bounds in the convex distance ⋮ Stein kernels and moment maps ⋮ Regularization lemmas and convergence in total variation ⋮ The optimal fourth moment theorem ⋮ Stein's method, logarithmic Sobolev and transport inequalities ⋮ Stein meets Malliavin in normal approximation
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