A Link Between the Log-Sobolev Inequality and Lyapunov Condition
文献类型：期刊论文
| 作者 | Liu, Yuan
|
| 刊名 | POTENTIAL ANALYSIS
 |
| 出版日期 | 2016-05-01 |
| 卷号 | 44期号:4页码:629-637 |
| 关键词 | Log-Sobolev inequality Log-concave measure Heat flow Symmetric diffusion Lyapunov condition |
| ISSN号 | 0926-2601 |
| DOI | 10.1007/s11118-015-9522-1 |
| 英文摘要 | 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 I center dot-Lyapunov conditions were introduced by Cattiaux et al. (J. Funct. Anal. 256(6), 1821-1841 2009) to study functional inequalities, and the above result on LSI was first proved subject to phi(.) = d (2)(., x(0)) by Cattiaux et al. (Proba. Theory Relat. Fields 148(1-2), 285-304 2010) through a combination of detective L (2) transportation-information inequality W2I 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. |
| 语种 | 英语 |
| WOS记录号 | WOS:000374964500001 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/22567]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Liu, Yuan |
| 作者单位 | Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Liu, Yuan. A Link Between the Log-Sobolev Inequality and Lyapunov Condition[J]. POTENTIAL ANALYSIS,2016,44(4):629-637. |
| APA | Liu, Yuan.(2016).A Link Between the Log-Sobolev Inequality and Lyapunov Condition.POTENTIAL ANALYSIS,44(4),629-637. |
| MLA | Liu, Yuan."A Link Between the Log-Sobolev Inequality and Lyapunov Condition".POTENTIAL ANALYSIS 44.4(2016):629-637. |
入库方式： OAI收割
来源：数学与系统科学研究院
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