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- W1765305890 abstract "We give an alternative look at the log-Sobolev inequality (LSI in short) for log-concave measures by semigroup tools. The similar idea yields a heat flow proof of LSI under some quadratic Lyapunov condition for symmetric diffusions on Riemannian manifolds provided the Bakry-Emery's curvature is bounded from below. Let's mention that, the general $phi$-Lyapunov conditions were introduced by Cattiaux-Guillin-Wang-Wu [8] to study functional inequalities, and the above result on LSI was first proved subject to $phi(cdot)=d^2(cdot, x_0)$ by Cattiaux-Guillin-Wu [9] through a combination of detective $L^2$ transportation-information inequality $mathrm{W_2I}$ and the HWI inequality of Otto-Villani. Next, we assert a converse implication that the Lyapunov condition can be derived from LSI, which means their equivalence in the above setting." @default.
- W1765305890 created "2016-06-24" @default.
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- W1765305890 date "2014-10-22" @default.
- W1765305890 modified "2023-09-26" @default.
- W1765305890 title "A link between the log-Sobolev inequality and Lyapunov condition" @default.
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- W1765305890 doi "https://doi.org/10.48550/arxiv.1410.6080" @default.
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