On Some Possible Combinations of Mixing Rates for Strictly Stationary, Reversible Markov Chains

A class of examples is constructed to show that for strictly stationary Markov chains that are reversible, the simultaneous mixing rates for the ρ-mixing and strong mixing (α-mixing) conditions can be fairly arbitrary, within certain unavoidable tight restrictions. The examples constructed here have the added property that the mixing rate for the absolute regularity (β-mixing) condition is within a constant factor of that for strong mixing.