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A Probabilistic Proof of the Fundamental Gap Conjecture Via the Coupling by Reflection
Gong, Fuzhou1; Li, Huaiqian2; Luo, Dejun1
2016-04-01
Source PublicationPOTENTIAL ANALYSIS
ISSN0926-2601
Volume44Issue:3Pages:423-442
AbstractLet 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.
KeywordSchrodinger operator Spectral gap Ground state Coupling by reflection Logarithmic Sobolev inequality
DOI10.1007/s11118-015-9476-3
Language英语
Funding ProjectKey Laboratory of RCSDS ; CAS[2008DP173182] ; NSFC[11021161] ; NSFC[11401403] ; NSFC[11101407] ; 973 Project[2011CB808000] ; Australian Research Council (ARC)[DP130101302] ; AMSS[Y129161ZZ1]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000374865700001
PublisherSPRINGER
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/22588
Collection应用数学研究所
Affiliation1.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
Recommended Citation
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.
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