混合下传输不等式与受限对数Sobolev不等式的稳定性
Stability under mixtures of transportation inequalities and restricted log-Sobolev inequalities
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- University of Warsaw（华沙大学）
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中文总结 AI 辅助
本文研究传输-熵不等式与受限泛函不等式在混合下的稳定性，给出将不等式从混合分量转移到混合本身的充分条件。
中文摘要 AI 辅助
我们证明了关于传输-熵不等式以及Poincaré和log-Sobolev型受限泛函不等式在混合下的稳定性结果。我们处理了$\u0054_2$和$\u0054_1$型Talagrand不等式及其推广，以及Gozlan等人引入的弱传输不等式。我们的主要结果提供了温和的充分条件，在这些条件下，给定的不等式可以从混合分量转移到混合本身。
英文摘要
We prove results about stability under mixtures for transport--entropy inequalities and restricted functional inequalities of Poincaré and log-Sobolev type. We treat Talagrand inequalities of type $\mathbf{T}_2$ and $\mathbf{T}_1$ together with their generalizations, as well as weak transportation inequalities introduced by Gozlan et al. Our main results provide mild sufficient conditions under which a given inequality may be transferred from mixture components to the mixture itself.
