If we then look at path coupling of $X_t,Y_t$ s.t. de l'Union Interbalkanique 2, 77–105 (1937), Freedman, D.: Markov Chains. Ann. << << Would we still analyze the same $\tau$ to get an upper bound? You are correct in saying that you don't need monotonicity to prove that coupling inequality. /BBox [0 0 5669.291 8] /Type /XObject /Resources 20 0 R /Length 15 >> /Matrix [1 0 0 1 0 0] << [To appear in J. Appl. << Quick link too easy to remove after installation, is this a problem? /Matrix [1 0 0 1 0 0] San Francisco: Holden Day 1971, Griffeath, D.: Coupling methods for nonhomogeneous Markov chains. Soc. ˽
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