AD-HMC achieves geometric convergence in Wasserstein distance for HMC with general asymmetrical auxiliary momentum distributions by restoring self-adjointness via direction alternation, with extensions to leapfrog integrators.
Curvature, concentration and error estimates for Markov chain Monte Carlo.Ann
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Derives matrix concentration inequalities for time-inhomogeneous Markov chains under positive Ollivier-Ricci curvature or Saloff-Coste-Zuniga spectral gap, illustrated on dynamic Bradley-Terry-Luce models.
The singular-value gap of a nonreversible Markov generator bounds finite-time variance of empirical averages uniformly over L2 functions and implies solvability of the Poisson equation when positive.
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Matrix concentration inequalities for time-inhomogeneous Markov chains
Derives matrix concentration inequalities for time-inhomogeneous Markov chains under positive Ollivier-Ricci curvature or Saloff-Coste-Zuniga spectral gap, illustrated on dynamic Bradley-Terry-Luce models.
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Singular-value gap of nonreversible Markov processes
The singular-value gap of a nonreversible Markov generator bounds finite-time variance of empirical averages uniformly over L2 functions and implies solvability of the Poisson equation when positive.