Efficient Markovian couplings: examples and counterexamples

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The Markov chain Monte Carlo revolution (2008, background): “The connections between coupling and eigenvalues is discussed in [12].”
On Neumann eigenfunctions in lip domains (2004, background): “Mirror couplings (without reflection) were used by Kendall ([17]) to obtain analytic estimates.”
Perfect simulation using dominating processes on ordered spaces, with application to locally stable point processes (2000, background): “In joint work with Burdzy one of us has begun to delineate the costs in terms of simulation time [4]; a further cost is that considerable care is required to make sure that the CFTP algorithm really is coalescing towards the correct process, and hence that one really is sampling perfectly from the t”
Scaling coupling of reflecting Brownian motions and the hot spots problem (2002, background): “There are two main known types of coupling of reecting planar Brownian motions in the literature: synchronous and mirror couplings (see [ BK ] for a discussion of these couplings).”