The partition function of the Bures ensemble as the tau-function of BKP and DKP hierarchies: continuous and discrete

doi:10.1088/1751-8121/aa7395

	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-Hao 1,2
	2017-07-14
发表期刊	JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
ISSN	1751-8113
卷号	50 期号:28 页码:20
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.
关键词	Toda-type equation matrix integrals Pfaffian BKP and DKP hierarchies
DOI	10.1088/1751-8121/aa7395
语种	英语
资助项目	National Natural Science Foundation of China[11331008] ; National Natural Science Foundation of China[11571358]
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary ; Physics, Mathematical
WOS记录号	WOS:000403935600001
出版者	IOP PUBLISHING LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25835
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.