High-dimensional MCMC with a standard splitting scheme for the underdamped Langevin diffusion.

The efficiency of a Markov sampler based on the underdamped Langevin diffusion is studied for high dimensional targets with convex and smooth potentials. We consider classical second-order integrator which requires only one gradient computation per iteration. Contrary to previous works similar samplers, dimension-free contraction Wasserstein distances convergence rate total variance distance are proven discrete time chain itself. Non-asymptotic variation bounds concentration inequalities obtained both Metropolis adjusted unadjusted chains. In particular, chain, in terms dimension d desired accuracy ε, order d∕ε general case, if Hessian potential Lipschitz, d1∕4∕ε case separable target, accordance known results other kinetic or HMC schemes.