On contraction properties of Markov kernels

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Strong Data Processing Inequalities and $\Phi $ -Sobolev Inequalities for Discrete Channels (2014, methodology): “To prove the second inequality, we borrow (and slightly streamline) an ingenious idea from [10].”
The Right Complexity Measure in Locally Private Estimation: It is not the Fisher Information (2018, background): “Such contractive properties have been important in the study of information channels [12, 14], where one studies strong data processing inequalities, and in the mixing properites of Markov chains under so-called strong mixing conditions , such as the Dobrushin condition [15].”
Yet Another Look at Harris’ Ergodic Theorem for Markov Chains (2008, methodology): “There have been other variations which have made use of Poisson equations or worked at getting explicit constants [KM05, DMR04, DMLM03 ].”