For diffusions on Riemannian manifolds with boundary, the paper establishes a quantitative space-time divergence lemma and proves that randomized Hamiltonian Monte Carlo and Langevin dynamics achieve the optimal square-root reduction in relaxation time.
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Space-time divergence lemmas and optimal non-reversible lifts of diffusions on Riemannian manifolds with boundary
For diffusions on Riemannian manifolds with boundary, the paper establishes a quantitative space-time divergence lemma and proves that randomized Hamiltonian Monte Carlo and Langevin dynamics achieve the optimal square-root reduction in relaxation time.