Covariance representations, \(L^p\)-Poincaré inequalities, Stein's kernels, and high-dimensional CLTs

DOI10.1007/978-3-031-26979-0_1arXiv2204.01088OpenAlexW4379409854MaRDI QIDQ6191328

Publication date: 7 March 2024

Published in: Progress in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.01088

zbMATH Keywords

Stein's method stable laws Poincaré inequality infinite divisibility log-concave measure covariance representations Bismut-type formulas high-dimensional CLTs

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Markov semigroups and applications to diffusion processes (47D07) Inequalities involving derivatives and differential and integral operators (26D10) Fractional partial differential equations (35R11)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Heat kernels and analyticity of non-symmetric jump diffusion semigroups
Approaching the Kannan-Lovász-Simonovits and variance conjectures
On Stein's method for infinite-dimensional Gaussian approximation in abstract Wiener spaces
A multivariate CLT for decomposable random vectors with finite second moments
On the theory of general partial differential operators
On the rate of convergence in the multivariate CLT
Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition
Multivariate normal approximation using Stein's method and Malliavin calculus
Weighted Poincaré-type inequalities for Cauchy and other convex measures
Second order Poincaré inequalities and CLTs on Wiener space
Functional analysis, Sobolev spaces and partial differential equations
Characterization of probability distributions by Poincaré-type inequalities
Stein's method for diffusion approximations
Dirichlet operators: A priori estimates and the uniqueness problem
On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
Interpolation, correlation identities, and inequalities for infinitely divisible variables
Isoperimetric constants for product probability measures
On improved Sobolev embedding theorems
Isoperimetric and analytic inequalities for log-concave probability measures
Classical Dirichlet forms on topological vector spaces --- closability and a Cameron-Martin formula
Concentration and deviation inequalities in infinite dimensions via covariance representations
On the rate of convergence in the entropic central limit theorem
Fisher information inequalities and the central limit theorem
Covariance identities and inequalities for functionals on Wiener and Poisson spaces
A multivariate CLT for local dependence with \(n^{-1/2}\log n\) rate and applications to multivariate graph related statistics
Entropy, reversible diffusion processes and Markov uniqueness
Transportation cost for Gaussian and other product measures
Asymmetric covariance estimates of Brascamp-Lieb type and related inequalities for log-concave measures
Stein's method in high dimensions with applications
Intertwinings and generalized Brascamp-Lieb inequalities
An almost constant lower bound of the isoperimetric coefficient in the KLS conjecture
Approximation of Hilbert-valued gaussians on Dirichlet structures
Modified log-Sobolev inequalities, Beckner inequalities and moment estimates
Multivariate normal approximation on the Wiener space: new bounds in the convex distance
Bourgain's slicing problem and KLS isoperimetry up to polylog
New error bounds in multivariate normal approximations via exchangeable pairs with applications to Wishart matrices and fourth moment theorems
On the equivalence of Sobolev norms in Malliavin spaces
Stein's method for normal approximation in Wasserstein distances with application to the multivariate central limit theorem
The CLT in high dimensions: quantitative bounds via martingale embedding
High-dimensional central limit theorems by Stein's method
On Stein's method for multivariate self-decomposable laws
Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula
Existence of Stein kernels under a spectral gap, and discrepancy bounds
A multivariate Berry-Esseen theorem with explicit constants
\(\Phi\)-entropy inequalities and asymmetric covariance estimates for convex measures
Stein kernels and moment maps
Stein's method, logarithmic Sobolev and transport inequalities
Functional inequalities for Gaussian convolutions of compactly supported measures: explicit bounds and dimension dependence
A stroll along the gamma
A high-dimensional CLT in \(\mathcal {W}_2\) distance with near optimal convergence rate
On the isoperimetric constant, covariance inequalities and \(L_{p}\)-Poincaré inequalities in dimension one
On Stein's method for multivariate self-decomposable laws with finite first moment
Normal Approximations with Malliavin Calculus
On Stein’s method for multivariate normal approximation
The LÉvy representation of the characteristic function of the probability density Γ(m+d/2){πd/2Γ(m)}-1(1+|x||x|2)-m-d/2
On an Inequality and a Related Characterization of the Normal Distribution
Poincaré-type inequalities via stochastic integrals
Central Limit Theorem in high dimensions: The optimal bound on dimension growth rate
Asymptotic estimates of multi-dimensional stable densities and their applications
On Stein's Method for Infinitely Divisible Laws with Finite First Moment
Multivariate normal approximations by Stein's method and size bias couplings
Entropy jumps for isotropic log-concave random vectors and spectral gap
Analysis and Geometry of Markov Diffusion Operators
Higher-order Stein kernels for Gaussian approximation
A Lyapunov-type Bound in R^d
Weak Poincaré inequalities and \(L^2\)-convergence rates of Markov semigroups
Spectral gap for spherically symmetric \(\log\)-concave probability measures, and beyond

This page was built for publication: Covariance representations, \(L^p\)-Poincaré inequalities, Stein's kernels, and high-dimensional CLTs