Concentration of empirical distribution functions with applications to non-i.i.d. models
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Publication:627308
DOI10.3150/10-BEJ254zbMath1207.62106arXiv1011.6165MaRDI QIDQ627308
Friedrich Götze, Sergey G. Bobkov
Publication date: 28 February 2011
Published in: Bernoulli (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1011.6165
random matriceslogarithmic Sobolev inequalitiesspectral distributionsPoincaré-type inequalitiesempirical measures
Multivariate distribution of statistics (62H10) Inequalities; stochastic orderings (60E15) Order statistics; empirical distribution functions (62G30) Large deviations (60F10) Approximations to statistical distributions (nonasymptotic) (62E17) Random matrices (algebraic aspects) (15B52)
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On concentration of empirical measures and convergence to the semi-circle law, Second order concentration via logarithmic Sobolev inequalities, One-dimensional empirical measures, order statistics, and Kantorovich transport distances, Uniform Chernoff and Dvoretzky-Kiefer-Wolfowitz-type inequalities for Markov chains and related processes
Cites Work
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- Random matrices: universality of local eigenvalue statistics
- Poincaré's inequalities and Talagrand's concentration phenomenon for the exponential distribution
- Local semicircle law and complete delocalization for Wigner random matrices
- The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality
- Weighted Poincaré-type inequalities for Cauchy and other convex measures
- Some deviation inequalities
- Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
- On tail probabilities of Kolmogorov-Smirnov statistics based on uniform mixing processes
- Isoperimetric constants for product probability measures
- Weak convergence of multidimensional empirical processes for stationary \(\varphi\)-mixing processes
- Rate of convergence to the semi-circular law
- Isoperimetric and analytic inequalities for log-concave probability measures
- Concentration of the spectral measure for large matrices
- Universality at the edge of the spectrum in Wigner random matrices.
- Hypercontractivity of Hamilton-Jacobi equations.
- A new method for bounding rates of convergence of empirical spectral distributions
- Gaussian fluctuations of eigenvalues in the GUE
- On concentration of empirical measures and convergence to the semi-circle law
- Rate of convergence to the semi-circle law for the deformed Gaussian unitary Ensemble
- The rate of convergence for spectra of GUE and LUE matrix ensembles
- Majorizing measures: The generic chaining
- The Wasserstein distance and approximation theorems
- Asymptotic Minimax Character of the Sample Distribution Function and of the Classical Multinomial Estimator
- Hardy Type Inequalities via Riccati and Sturm–Liouville Equations
- A Topological Application of the Isoperimetric Inequality
- Logarithmically concave functions and sections of convex sets in $R^{n}$
- Slicing Convex Bodies-Bounds for Slice Area in Terms of the Body's Covariance
- Weak convergence of multidimensional empirical processes for strong mixing sequences of stochastic vectors
- Inequalities for E k(X, Y) when the marginals are fixed
- Calculation of the Wasserstein Distance Between Probability Distributions on the Line
- The Rate of Convergence in Probability for Spectra of the GUE
- Deviation Inequalities on Largest Eigenvalues
- Hardy's inequality with weights
