A Note on Wasserstein-2 Error of Langevin Monte Carlo Under Strong Log-Concavity

This note refines a recent nonasymptotic bound on the Wasserstein error of Langevin Monte Carlo for strongly log-concave target distributions. The refinement preserves the linear dependence on the step size while accounting more precisely for the spectrum of the Hessian. For a representative spiked Gaussian model, the resulting bound improves the dimension dependence of the previous linear-in-step-size estimate from order $p^{3/2}$ to order $p$.