PreprintCC BY 4.0arXiv
Couplings Farthest from the Independent Gaussian
Abstract
Motivated by Wasserstein measures of dependence, we study the largest possible 2-Wasserstein distance between a joint distribution and the product of its prescribed marginals. For two uniform marginals, Catalano and Lavenant conjectured that the monotone and antimonotone couplings maximize the distance from the independent coupling. We prove the Gaussian analogue for an arbitrary number n≥ 2 of one-dimensional standard Gaussian marginals. More generally, for every probability measure μ on ℝ with finite second moment, we characterize the laws on ℝn with all marginals equal to μ that are farthest from the n-dimensional standard Gaussian.
Related
- Convergence of Kikuchi matrices to Γ-independent and q-Gaussian limits
- Copulas farthest from independence in quadratic Wasserstein distance
- Quasi-uniform designs from random candidates: optimal candidate complexity and farthest-point sampling
- Farthest-cell triplet entropy: high-dimensional shell limits and hyperbolic curvature amplification
- Optimal Couplings of Levy Processes in the Class of Immersion Couplings
BibTeX
@misc{schrott2026couplings,
title = {{Couplings Farthest from the Independent Gaussian}},
author = {Stefan Schrott},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10467},
eprint = {2609.10467},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10467},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Couplings Farthest from the Independent Gaussian
AU - Stefan Schrott
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10467
UR - https://arxiv.org/abs/2609.10467
AB - Motivated by Wasserstein measures of dependence, we study the largest possible 2-Wasserstein distance between a joint distribution and the product of its prescribed marginals. For two uniform marginals, Catalano and Lavenant conjectured that the monotone and antimonotone couplings maximize the distance from the independent coupling. We prove the Gaussian analogue for an arbitrary number n≥ 2 of one-dimensional standard Gaussian marginals. More generally, for every probability measure μ on ℝ with finite second moment, we characterize the laws on ℝ^n with all marginals equal to μ that are farthest from the n-dimensional standard Gaussian.
ER -