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Uniform-in-$N$ log-Sobolev inequality for the mean-field Langevin dynamics with convex energy (2409.10440v1)
Published 16 Sep 2024 in math.PR
Abstract: We establish a log-Sobolev inequality for the stationary distribution of mean-field Langevin dynamics with a constant that is independent of the number of particles $N$. Our proof proceeds by establishing the existence of a Lipschitz transport map from the standard Gaussian measure via the reverse heat flow of Kim and Milman.
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