具有凸能量的均场朗格文动力学的均匀-N$对数-索博列夫不等式

arXiv - MATH - Probability Pub Date : 2024-09-16 DOI:arxiv-2409.10440

Sinho Chewi, Atsushi Nitanda, Matthew S. Zhang

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摘要

我们为平均场朗格文动力学的静态分布建立了一个对数-索博列夫不等式，其常数与粒子数 $N$ 无关。我们的证明是通过 Kim 和 Milman 的反向热流，从标准高斯量度建立利普希兹传输映射的存在性。

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Uniform-in-$N$ log-Sobolev inequality for the mean-field Langevin dynamics with convex energy

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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arXiv - MATH - Probability

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