A Link Between the Log-Sobolev Inequality and Lyapunov Condition

doi:10.1007/s11118-015-9522-1

CSpace > 应用数学研究所

	A Link Between the Log-Sobolev Inequality and Lyapunov Condition
	Liu, Yuan
	2016-05-01
发表期刊	POTENTIAL ANALYSIS
ISSN	0926-2601
卷号	44 期号:4 页码:629-637
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.
关键词	Log-Sobolev inequality Log-concave measure Heat flow Symmetric diffusion Lyapunov condition
DOI	10.1007/s11118-015-9522-1
语种	英语
资助项目	NSFC[11201456] ; NSFC[1143000182] ; CAS[Y129161ZZ1] ; Key Laboratory of Random Complex Structures and Data, Academy of Mathematics and Systems Science, Chinese Academy of Sciences[2008DP173182]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000374964500001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/22568
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.