Pairwise optimal coupling of multiple random variables
Probability
2021-05-10 v2 Combinatorics
Abstract
We generalize the optimal coupling theorem to multiple random variables: Given a collection of random variables, it is possible to couple all of them so that any two differ with probability comparable to the total-variation distance between them. In a number of cases we show that the disagreement probability we achieve is the best possible. The proofs of sharpness rely on new results in extremal combinatorics, which may be of independent interest.
Cite
@article{arxiv.1903.00632,
title = {Pairwise optimal coupling of multiple random variables},
author = {Omer Angel and Yinon Spinka},
journal= {arXiv preprint arXiv:1903.00632},
year = {2021}
}
Comments
18 pages, 4 figures. Revised introduction. Improved and simplified some results and proofs