Sharp equivalence between ρ- and τ-mixing coefficients

Rémi Peyre. "Sharp equivalence between ρ- and τ-mixing coefficients." Studia Mathematica 216.3 (2013): 245-270. <http://eudml.org/doc/285835>.

@article{RémiPeyre2013,
abstract = {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.},
author = {Rémi Peyre},
journal = {Studia Mathematica},
keywords = {-mixing; $\tau $-mixing},
language = {eng},
number = {3},
pages = {245-270},
title = {Sharp equivalence between ρ- and τ-mixing coefficients},
url = {http://eudml.org/doc/285835},
volume = {216},
year = {2013},
}

TY - JOUR
AU - Rémi Peyre
TI - Sharp equivalence between ρ- and τ-mixing coefficients
JO - Studia Mathematica
PY - 2013
VL - 216
IS - 3
SP - 245
EP - 270
AB - 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.
LA - eng
KW - -mixing; $\tau $-mixing
UR - http://eudml.org/doc/285835
ER -