Constructing processes with prescribed mixing coefficients

This paper deals with η-mixing, a notion defined in [Kontorovich, Leonid, Ramanan, Kavita, 2008. Concentration inequalities for dependent random variables via the martingale method. Ann. Probab. (in press)], which is closely related to ϕ-mixing. We show that there exist measures on finite sequences with essentially arbitrary η-mixing coefficients, as well as processes with arbitrarily slow mixing rates.