A note on two measures of dependence

In a paper in 1956, Dobrushin proved a central limit theorem for triangular arrays of Markov chains under certain dependence assumptions somewhat related to “Doeblin’s condition”. In a very recent paper, Peligrad proved a central limit theorem of the same type, but with dependence assumptions based on maximal correlations. This note here will give a concrete example to illustrate the extent to which Peligrad’s result goes beyond that of Dobrushin.