| Abstract: |
| We describe the classical Markov couplings of Riemannian Brownian motions and how these natural constructions fail in sub-Riemannian geometry, even for the simplest case of the Heisenberg group. After reviewing the situation, we describe an improvement and extension of recent constructions of non-adapted reflection couplings on sub-Riemannian model spaces by Banerjee-Gordina-Mariano and B\`en\`efice. Moreover, this construction is relatively simple and geometrically appealing, being based on global symmetries of the underlying spaces. |
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