Truncations of Random Unitary Matrices Drawn from Hua-Pickrell Distribution | |
Lin, Zhaofeng2; Qiu, Yanqi1,3; Wang, Kai4 | |
刊名 | COMPLEX ANALYSIS AND OPERATOR THEORY |
2023 | |
卷号 | 17期号:1页码:24 |
关键词 | Determinantal point process Hua-Pickrell measure Truncated unitary matrix Limiting point process Weighted Bergman kernel |
ISSN号 | 1661-8254 |
DOI | 10.1007/s11785-022-01306-8 |
英文摘要 | 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. |
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 |
语种 | 英语 |
出版者 | SPRINGER BASEL AG |
WOS记录号 | WOS:000894412300001 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60537] |
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.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China 2.Fudan Univ, Shanghai Ctr Math Sci, Shanghai 200438, 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. |
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