I have seen properties named ρ-, β-, and α-mixing conditions in papers related to Copulas and Markov processes like this one:

> In this paper, we identify conditions on C that suffice for
> geometrically fast mixing rates. Geometric β-mixing, equivalent to
> geometric ergodicity for sta- tionary Markov chains, is established
> under a rather strong condition that ex- cludes copulas that exhibit
> tail dependence or asymmetry.Geometric ρ-mixing, which implies
> geometric α-mixing, is obtained under a much weaker condition. We
> verify this condition for various parametric copula functions that are
> pop- ular in applied work. ρ-, β-, and α-mixing conditions may be used
> as the basis for a range of inequalities and limit theorems that are
> useful in demonstrating the asymptotic validity of statistical
> methods;

[Beare, B., 2010, Copulas and temporal dependence, Econometrica, 78(1).][1]


I am an engineering student and I have trouble understanding these conditions in statistical texts. Can somebody explain them?
Thanks


  [1]: https://escholarship.org/uc/item/87p829d4