Wasserstein gradient flows of linearly convex objectives with an entropy term converge at explicit rates: O(1/t) under plain convexity, and arbitrarily fast polynomial or exponential rates under entropy-strong convexity.
Some estimates of the transition density of a nondegenerate diffusion Markov process
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Convergence of drift-diffusion PDEs arising as Wasserstein gradient flows of convex functions
Wasserstein gradient flows of linearly convex objectives with an entropy term converge at explicit rates: O(1/t) under plain convexity, and arbitrarily fast polynomial or exponential rates under entropy-strong convexity.