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Uniform log-Sobolev inequalities for mean field particles with flat-convex energy

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arxiv 2408.03283 v2 pith:IBY3H47H submitted 2024-08-06 math.PR

Songbo Wang This is my paper · ORCID
classification math.PR
keywords uniformenergyfieldinequalitiesinequalitylog-sobolevmeanparticle
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The purpose of this short note is to demonstrate uniform logarithmic Sobolev inequalities for the mean field gradient particle systems associated to an energy functional that is convex in the flat sense. A defective log-Sobolev inequality was already established implicitly in a previous joint work with F. Chen and Z. Ren [arXiv:2212.03050 [math.PR]]. It remains only to tighten it by a uniform Poincar\'e inequality, which we prove by the method in a recent work of Guillin, W. Liu, L. Wu and C. Zhang [Ann. Appl. Probab., 32(3):1590-1614, 2022]. As an application, we show that the particle system exhibits the concentration of measure phenomenon in the long time.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The ballistic limit of the log-Sobolev constant equals the Polyak-{\L}ojasiewicz constant

    math.PR 2024-11 accept novelty 8.0 of 10

    The low-temperature ratio of the log-Sobolev constant to temperature converges to the Polyak-Lojasiewicz constant of the potential.

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    math.OC 2024-11 conditional novelty 7.0 of 10

    Linear convergence of JKO-based proximal point, prox-linear, and proximal gradient schemes is proved for entropy-regularized flat-convex functionals, with iterates shown to have finite relative Fisher information.

  3. Non-asymptotic entropic bounds for non-linear kinetic Langevin sampler with second-order splitting scheme

    math.PR 2024-12 conditional novelty 6.0 of 10

    A non-asymptotic relative entropy bound for unadjusted kinetic Langevin Monte Carlo with a second-order splitting scheme, under defective log-Sobolev and Lyapunov conditions more general than prior work.

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