Empirical measures and random walks on compact spaces in the quadratic Wasserstein metric

DOI10.1214/22-aihp1322zbMath1530.60041arXiv2110.00295OpenAlexW3203438058MaRDI QIDQ6147698

Publication date: 16 January 2024

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.00295

zbMATH Keywords

Riemannian manifold Lie group occupation measure heat kernel Berry-Esseen inequality optimal transportation

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Sums of independent random variables; random walks (60G50) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Optimal transportation (49Q22)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
A spectral gap theorem in simple Lie groups
Random walks in compact groups
Simple bounds for the convergence of empirical and occupation measures in 1-Wasserstein distance
On the rate of convergence in Wasserstein distance of the empirical measure
Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary \(\alpha\)-dependent sequences
A spectral gap theorem in SU\((d)\)
Transport inequalities on Euclidean spaces for non-Euclidean metrics
The Ruziewicz problem and distributing points on homogeneous spaces of a compact Lie group
Ergodicity and exponential \(\beta\)-mixing bounds for multidimensional diffusions with jumps
Basic properties of strong mixing conditions. A survey and some open questions
On optimal matchings
Matching random samples in many dimensions
On polynomial mixing bounds for stochastic differential equations
A PDE approach to a 2-dimensional matching problem
Riemannian manifolds with uniformly bounded eigenfunctions
Automorphic forms and the distribution of points on odd-dimensional spheres.
Foundations of quantization for probability distributions
Equidistribution of random walks on compact groups. II: The Wasserstein metric
A Wasserstein inequality and minimal Green energy on compact manifolds
A simple Fourier analytic proof of the AKT optimal matching theorem
Wasserstein distance, Fourier series and applications
Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\)
Berry-Esseen smoothing inequality for the Wasserstein metric on compact Lie groups
Approximation by finitely supported measures
Some Limit Theorems for Random Functions. I
Symmetric Random Walks on Groups
Hecke operators and distributing points on the sphere I
Hecke operators and distributing points on S². II
Probabilities on a Compact Group
On the Wasserstein distance between classical sequences and the Lebesgue measure
Subgeometric ergodicity and β-mixing
One-dimensional empirical measures, order statistics, and Kantorovich transport distances
Comparison between W₂ distance and Ḣ⁻¹ norm, and Localization of Wasserstein distance

This page was built for publication: Empirical measures and random walks on compact spaces in the quadratic Wasserstein metric