Truncations of Random Unitary Matrices Drawn from Hua-Pickrell Distribution

doi:10.1007/s11785-022-01306-8

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	Truncations of Random Unitary Matrices Drawn from Hua-Pickrell Distribution
	Lin, Zhaofeng 1; Qiu, Yanqi 2,3; Wang, Kai 4
	2023
发表期刊	COMPLEX ANALYSIS AND OPERATOR THEORY
ISSN	1661-8254
卷号	17 期号:1 页码:24
摘要	Let U be a random unitary matrix drawn from the Hua-Pickrell distribution mu(U)(n+m)((delta)) on the unitary group U(n + m). We show that the eigenvalues of the truncated unitary matrix [U-i,U- j](1 <= i, j <= n) form a determinantal point process X-n((m,delta)) non the unit disc D for any delta is an element of C satisfying Re delta > -1/2. We also prove that the limiting point process taken by n -> infinity of the determinantal point process X(n)((m,delta) )is always X-[m], independent of delta. Here X[m] is the determinantal point process on 13 with weighted Bergman kernel K-[m](z, w) = 1/(1 - z <(w)over bar >)(m+1) with respect to the reference measure d mu([m])(z) = m/pi (1 - \|z\|)(m-1)d sigma (z), where d sigma (z) is the Lebesgue measure on D.
关键词	Determinantal point process Hua-Pickrell measure Truncated unitary matrix Limiting point process Weighted Bergman kernel
DOI	10.1007/s11785-022-01306-8
收录类别	SCI
语种	英语
资助项目	NSFC[Y7116335K1] ; NSFC[11801547] ; NSFC[11688101] ; NSFC[12231005] ; NSFC[12026250] ; NSFC[11722102] ; Shanghai Technology Innovation Project[21JC1400800]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000894412300001
出版者	SPRINGER BASEL AG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60538
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Kai
作者单位	1.Fudan Univ, Shanghai Ctr Math Sci, Shanghai 200438, Peoples R China 2.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China 3.Chinese Acad Sci, Inst Math, AMSS, Beijing 100190, Peoples R China 4.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Lin, Zhaofeng,Qiu, Yanqi,Wang, Kai. Truncations of Random Unitary Matrices Drawn from Hua-Pickrell Distribution[J]. COMPLEX ANALYSIS AND OPERATOR THEORY,2023,17(1):24.
APA	Lin, Zhaofeng,Qiu, Yanqi,&Wang, Kai.(2023).Truncations of Random Unitary Matrices Drawn from Hua-Pickrell Distribution.COMPLEX ANALYSIS AND OPERATOR THEORY,17(1),24.
MLA	Lin, Zhaofeng,et al."Truncations of Random Unitary Matrices Drawn from Hua-Pickrell Distribution".COMPLEX ANALYSIS AND OPERATOR THEORY 17.1(2023):24.