A Probabilistic Proof of the Fundamental Gap Conjecture Via the Coupling by Reflection

doi:10.1007/s11118-015-9476-3

CSpace > 应用数学研究所

	A Probabilistic Proof of the Fundamental Gap Conjecture Via the Coupling by Reflection
	Gong, Fuzhou1 ; Li, Huaiqian 2; Luo, Dejun1
	2016-04-01
发表期刊	POTENTIAL ANALYSIS
ISSN	0926-2601
卷号	44 期号:3 页码:423-442
摘要	Let be a strictly convex domain with smooth boundary and diameter D. The fundamental gap conjecture claims that if is convex, then the spectral gap of the Schrodinger operator -Delta+V with Dirichlet boundary condition is greater than . Using analytic methods, Andrews and Clutterbuck recently proved in (J. Amer. Math. Soc. 24(3), 889-916 2011) a more general spectral gap comparison theorem which implies this conjecture. In the first part of the current work, we shall give a probabilistic proof of their result via the coupling by reflection of the diffusion processes. Moreover, we also present in the second part a simpler probabilistic proof of the original conjecture.
关键词	Schrodinger operator Spectral gap Ground state Coupling by reflection Logarithmic Sobolev inequality
DOI	10.1007/s11118-015-9476-3
语种	英语
资助项目	Key Laboratory of RCSDS ; CAS[2008DP173182] ; NSFC[11021161] ; NSFC[11401403] ; NSFC[11101407] ; 973 Project[2011CB808000] ; Australian Research Council (ARC)[DP130101302] ; AMSS[Y129161ZZ1]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000374865700001
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/22588
专题	应用数学研究所
通讯作者	Luo, Dejun
作者单位	1.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China
推荐引用方式 GB/T 7714	Gong, Fuzhou,Li, Huaiqian,Luo, Dejun. A Probabilistic Proof of the Fundamental Gap Conjecture Via the Coupling by Reflection[J]. POTENTIAL ANALYSIS,2016,44(3):423-442.
APA	Gong, Fuzhou,Li, Huaiqian,&Luo, Dejun.(2016).A Probabilistic Proof of the Fundamental Gap Conjecture Via the Coupling by Reflection.POTENTIAL ANALYSIS,44(3),423-442.
MLA	Gong, Fuzhou,et al."A Probabilistic Proof of the Fundamental Gap Conjecture Via the Coupling by Reflection".POTENTIAL ANALYSIS 44.3(2016):423-442.