INSTABILITY RESULTS FOR THE LOGARITHMIC SOBOLEV INEQUALITY AND ITS APPLICATION TO RELATED INEQUALITIES

Kim Daesung

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INSTABILITY RESULTS FOR THE LOGARITHMIC SOBOLEV INEQUALITY AND ITS APPLICATION TO RELATED INEQUALITIES

机译：INSTABILITY RESULTS FOR THE LOGARITHMIC SOBOLEV INEQUALITY AND ITS APPLICATION TO RELATED INEQUALITIES

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摘要

We show that there are no general stability results for the logarithmic Sobolev inequality in terms of the Wasserstein distances and L-p(d gamma) distance for p > 1. To this end, we construct a sequence of centered probability measures such that the deficit of the logarithmic Sobolev inequality converges to zero but the relative entropy and the moments do not, which leads to instability for the logarithmic Sobolev inequality. As an application, we prove instability results for Talagrand's transportation inequality and the Beckner-Hirschman inequality.

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《Discrete and continuous dynamical systems》 |2022年第9期|4297-4320|共24页
作者
Kim Daesung;
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作者单位

Univ Illinois;

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正文语种英语
中图分类理论力学（一般力学）;
关键词
The logarithmic Sobolev inequality; Talagrand's inequality; the Beckner-Hirschman inequality; the entropic uncertainty principle; MASS-TRANSPORT; STABILITY; DEFICIT; TALAGRAND;

INSTABILITY RESULTS FOR THE LOGARITHMIC SOBOLEV INEQUALITY AND ITS APPLICATION TO RELATED INEQUALITIES

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