Under LSI and convexity assumptions on the target, the relative entropy of underdamped Langevin dynamics decays at an explicit rate proportional to sqrt(ρ) with constant depending on a scaled friction parameter.
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An explicit rate Λ = 1/(6(√(2 + K/(2m)) + √(4 + K/(2m)))) √m is proven for L2 convergence of underdamped Langevin dynamics, recovering the optimal O(√m) order when the potential is convex.
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A sharp hypocoercive entropy decay estimate for underdamped Langevin dynamics
Under LSI and convexity assumptions on the target, the relative entropy of underdamped Langevin dynamics decays at an explicit rate proportional to sqrt(ρ) with constant depending on a scaled friction parameter.
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Sharp hypocoercive convergence estimates for underdamped Langevin dynamics via the modified $L^2$ method
An explicit rate Λ = 1/(6(√(2 + K/(2m)) + √(4 + K/(2m)))) √m is proven for L2 convergence of underdamped Langevin dynamics, recovering the optimal O(√m) order when the potential is convex.