A Probabilistic Proof of the Fundamental Gap Conjecture Via the Coupling by Reflection
文献类型：期刊论文
| 作者 | Gong, Fuzhou1 ; Li, Huaiqian2; Luo, Dejun1
|
| 刊名 | POTENTIAL ANALYSIS
 |
| 出版日期 | 2016-04-01 |
| 卷号 | 44期号:3页码:423-442 |
| 关键词 | Schrodinger operator Spectral gap Ground state Coupling by reflection Logarithmic Sobolev inequality |
| ISSN号 | 0926-2601 |
| DOI | 10.1007/s11118-015-9476-3 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000374865700001 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/22587]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。