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A Peskun ordering between two samplers, implying a dominance of one over the other, is known among the Markov chain Monte Carlo community for being a remarkably strong result, but it is also known for being one that is notably difficult to establish. Indeed, one has to prove that the probability to reach a state 𝐲 from state 𝐱, using a sampler, is greater than or equal to the probability using the other sampler, and this must hold for all pairs (𝐱, 𝐲) such that 𝐱≠𝐱. We provide in this paper aarXiv:2003.05492v3 fatcat:zho3vobxnrdu3jmprdvlcb2fuq