KMS Of Academy of mathematics and systems sciences, CAS
| A Probabilistic Proof of the Fundamental Gap Conjecture Via the Coupling by Reflection | |
Gong, Fuzhou1 ; Li, Huaiqian2; Luo, Dejun1
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| 2016-04-01 | |
| Source Publication | POTENTIAL ANALYSIS
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| ISSN | 0926-2601 |
| Volume | 44Issue:3Pages:423-442 |
| Abstract | 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. |
| Keyword | Schrodinger operator Spectral gap Ground state Coupling by reflection Logarithmic Sobolev inequality |
| DOI | 10.1007/s11118-015-9476-3 |
| Language | 英语 |
| Funding Project | Key Laboratory of RCSDS ; CAS[2008DP173182] ; NSFC[11021161] ; NSFC[11401403] ; NSFC[11101407] ; 973 Project[2011CB808000] ; Australian Research Council (ARC)[DP130101302] ; AMSS[Y129161ZZ1] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000374865700001 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/22588 |
| Collection | 应用数学研究所 |
| Corresponding Author | Luo, Dejun |
| Affiliation | 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 |
| 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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