Proves near-Lipschitz stability in 2-Wasserstein distance (up to log factor) and relative entropy stability for the Kim-Milman flow map w.r.t. target measure perturbations under regularity assumptions, with existence for finite second moment targets.
Propagation of weak log-concavity along generalised heat flows via Hamilton–Jacobi equations.arXiv preprint 2508.07931, August
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Near-Lipschitz stability of the Kim--Milman flow map
Proves near-Lipschitz stability in 2-Wasserstein distance (up to log factor) and relative entropy stability for the Kim-Milman flow map w.r.t. target measure perturbations under regularity assumptions, with existence for finite second moment targets.