For two σ-algebras 𝓐 and ℬ, the ρ-mixing coefficient ρ(𝓐,ℬ) between 𝓐 and ℬ is the supremum correlation between two real random variables X and Y which are 𝓐 - resp. ℬ-measurable; the τ'(𝓐,ℬ) coefficient is defined similarly, but restricting to the case where X and Y are indicator functions. It has been known for a long time that the bound ρ ≤ Cτ'(1 + en | log τ'|) holds for some constant C; in this article, we show that C = 1 works and is best possible.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-3-4,
author = {R\'emi Peyre},
title = {Sharp equivalence between $\rho$- and $\tau$-mixing coefficients},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {245-270},
zbl = {06195637},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-3-4}
}
Rémi Peyre. Sharp equivalence between ρ- and τ-mixing coefficients. Studia Mathematica, Tome 215 (2013) pp. 245-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-3-4/