On the Law of Large Numbers for the Empirical Measure Process of Generalized Dyson Brownian Motion
文献类型：期刊论文
| 作者 | Li, Songzi1; Li, Xiang-Dong2,3 ; Xie, Yong-Xiao4
|
| 刊名 | JOURNAL OF STATISTICAL PHYSICS
 |
| 出版日期 | 2020-09-21 |
| 页码 | 29 |
| 关键词 | Generalized Dyson Brownian motion McKean-Vlasov equation Gradient flow Optimal transportation Voiculescu free entropy Law of Large Numbers Propagation of chaos |
| ISSN号 | 0022-4715 |
| DOI | 10.1007/s10955-020-02627-8 |
| 英文摘要 | We study the generalized Dyson Brownian motion (GDBM) of an interacting N-particle system with logarithmic Coulomb interaction and general potential V. Under reasonable condition on V, we prove the existence and uniqueness of strong solution to SDE for GDBM. We then prove that the family of the empirical measures ofGDBMis tight on C([0, T], P(R)) and all the large N limits satisfy a nonlinear McKean-Vlasov equation. Inspired by previous works due to Biane and Speicher, Carrillo, McCann and Villani, and Blower, we prove that the McKean-Vlasov equation is indeed the gradient flow of the Voiculescu free entropy on the Wasserstein space of probability measures over R. Using the optimal transportation theory, we prove that if V '' >= K for some constant K is an element of R, the McKean-Vlasov equation has a unique weak solution in the space of probability measures P(R). This establishes the Law of Large Numbers and the propagation of chaos for the empirical measures of GDBM with non-quadratic external potentials which are not necessarily convex. Finally, we prove the longtime convergence of the McKean-Vlasov equation for C-2-convex potentials V. |
| 资助项目 | NSFC[11601287] ; NSFC[11771430] ; NSFC[11901569] ; Key Laboratory RCSDS, CAS[2008DP173182] |
| WOS研究方向 | Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000571672100001 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/52205]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Li, Xiang-Dong |
| 作者单位 | 1.Renmin Univ China, Sch Math, 59 Zhongguancun Da Jie, Beijing 100872, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, 55 Zhongguancun East Rd, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Shandong Normal Univ, Sch Math & Stat, 1 Univ Rd,Sci & Technol Pk, Jinan 250385, Peoples R China |
| 推荐引用方式 GB/T 7714 | Li, Songzi,Li, Xiang-Dong,Xie, Yong-Xiao. On the Law of Large Numbers for the Empirical Measure Process of Generalized Dyson Brownian Motion[J]. JOURNAL OF STATISTICAL PHYSICS,2020:29. |
| APA | Li, Songzi,Li, Xiang-Dong,&Xie, Yong-Xiao.(2020).On the Law of Large Numbers for the Empirical Measure Process of Generalized Dyson Brownian Motion.JOURNAL OF STATISTICAL PHYSICS,29. |
| MLA | Li, Songzi,et al."On the Law of Large Numbers for the Empirical Measure Process of Generalized Dyson Brownian Motion".JOURNAL OF STATISTICAL PHYSICS (2020):29. |
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。