I have seen properties named $\rho$-, $\beta$-, and $\alpha$-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 $\beta$-mixing, equivalent to geometric ergodicity for stationary Markov chains, is established under a rather strong condition that excludes copulas that exhibit tail dependence or asymmetry. Geometric $\rho$-mixing, which implies geometric $\alpha$-mixing, is obtained under a much weaker condition. We verify this condition for various parametric copula functions that are popular in applied work. $\rho$-, $\beta$-, and $\alpha$-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).

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