A coupling-based proof shows the Langevin transport map is Lipschitz with dimension-free constants under only asymptotic log-concavity and either bounded or Lipschitz Hessian of the potential.
Behavior of the Poincar´ e Constant alon g the Polchinski Renormalization Flow
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A coupling approach to Lipschitz transport maps
A coupling-based proof shows the Langevin transport map is Lipschitz with dimension-free constants under only asymptotic log-concavity and either bounded or Lipschitz Hessian of the potential.