The partition function of the Bures ensemble as the tau-function of BKP and DKP hierarchies: continuous and discrete | |
Hu, Xing-Biao1,2; Li, Shi-Hao1,2 | |
刊名 | JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL |
2017-07-14 | |
卷号 | 50期号:28页码:20 |
关键词 | Toda-type equation matrix integrals Pfaffian BKP and DKP hierarchies |
ISSN号 | 1751-8113 |
DOI | 10.1088/1751-8121/aa7395 |
英文摘要 | The relationship between matrix integrals and integrable systems was revealed more than 20 years ago. As is known, matrix integrals over a Gaussian ensemble used in random matrix theory could act as the tau-function of several hierarchies of integrable systems. In this article, we will show that the time-dependent partition function of the Bures ensemble, whose measure has many interesting geometric properties, could act as the tau-function of BKP and DKP hierarchies. In addition, if discrete time variables are introduced, then this partition function could act as the tau-function of discrete BKP and DKP hierarchies. In particular, there are some links between the partition function of the Bures ensemble and Toda-type equations. |
资助项目 | National Natural Science Foundation of China[11331008] ; National Natural Science Foundation of China[11571358] |
WOS研究方向 | Physics |
语种 | 英语 |
出版者 | IOP PUBLISHING LTD |
WOS记录号 | WOS:000403935600001 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/25834] |
专题 | 计算数学与科学工程计算研究所 |
通讯作者 | Li, Shi-Hao |
作者单位 | 1.Chinese Acad Sci, AMSS, Inst Computat Math & Sci Engn Comp, LSEC, POB 2719, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
推荐引用方式 GB/T 7714 | Hu, Xing-Biao,Li, Shi-Hao. The partition function of the Bures ensemble as the tau-function of BKP and DKP hierarchies: continuous and discrete[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL,2017,50(28):20. |
APA | Hu, Xing-Biao,&Li, Shi-Hao.(2017).The partition function of the Bures ensemble as the tau-function of BKP and DKP hierarchies: continuous and discrete.JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL,50(28),20. |
MLA | Hu, Xing-Biao,et al."The partition function of the Bures ensemble as the tau-function of BKP and DKP hierarchies: continuous and discrete".JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 50.28(2017):20. |
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