請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/6825完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張志中 | |
| dc.contributor.author | Chao-Hsiung Hsu | en |
| dc.contributor.author | 許朝雄 | zh_TW |
| dc.date.accessioned | 2021-05-17T09:18:55Z | - |
| dc.date.available | 2012-07-18 | |
| dc.date.available | 2021-05-17T09:18:55Z | - |
| dc.date.copyright | 2012-07-18 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-07-10 | |
| dc.identifier.citation | [1] A. Lytova and L.Pastur.(2009). Central limit theorem for linear eigenvalue statistics of random
matrices with independent entries. The Annals of Probability 2009, Vol.37, No.5 1778-1840. [2] La ́szlo ́ Erdo ̈s,Horng-Tzer Yau,and Jun Yin.(2010). Rigidity of eigenvalues of generalized Wigner matrices. Advances in Mathematics, Volume 229, Issue 3, 15 February 2012, Pages 1435-1515 [3] Arharov, L. V.(1971). Limit theorems for the characteristic roots of a sample covariance matrix.Dokl. Akad. Nauk. SSSR 199 994-997. [4] Greg W. Anderson, Alice Guionnet, and Ofer Zeitouni.(2009). An Introduction to random matrices. Cambridge Studies in Advanced Mathematics, 118, Cambridge University Press [5] L.Pastur.(2005). A simple approach to the global regime of Gaussian ensembles of random matrices. Ukrainian Math. J. 57, no. 6, 936-966 [6] Rick Durrett.(2005). Probability: Theory and Examples. 3rd edition. Duxbury advanced series. [7] S.R.S. Varadhan.(2001). Probability Theory. American Mathematical society. [8] Herman Chernoff.(1981). A note on an inequality involving the normal distribution. The Annals of Probability 1981, Vol.9, No.3 533-535. [9] Z. D. Bai and J. W. Silverstein.(2009). Spectral analysis of large dimensional random matrices. 2nd edition. Springer [10] Percy Deift.(2000). Orthogonal polynomials and random matrices: A Riemann-Hilbert approach. Courant Lecture Notes. AMS, 2000. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/6825 | - |
| dc.description.abstract | In this paper, we consider n×n real symmetric Wigner matrices W with independent (modulo symmetry condition), but not necessarily identically distributed, entries {W_jk }_(j,k=1)^n and prove central limit theorem for linear eigenvalue statistics of such matrices. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-17T09:18:55Z (GMT). No. of bitstreams: 1 ntu-101-R98221002-1.pdf: 336209 bytes, checksum: 6a8bea52e15602df9819252e86ab9cae (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | 口試委員會審定書………………………………………………………………….i
Acknowledgement…………………………………………………………………ii 中文摘要…………………………………………………………………………vi Abstract………………………………………………………………………………..v 1 Introduction to generalized Wigner matrices and other generalities……..………1 1.1 Introduction………………………………………………………….……1 1.2 Preliminaries…………………………………………………………………1 1.3 Lemmas…...……...………………..…………………………………………2 2 Central Limit Theorem for linear eigenvalue statistics in the case of Gaussian entries………….……………………………………………………11 2.1 Bound of Variance…………………………….…………………………….11 2.2 Central Limit Theorem………………………….………………………… .12 3 Central Limit Theorem for linear eigenvalue statistics in general cases…..26 3.1Generalities…………………………….…………………………….26 3.2 Central Limit Theorem in general cases..……….………………………… .28 References………………………………………………………………………32 | |
| dc.language.iso | zh-TW | |
| dc.title | 廣義隨機矩陣特徵值之中央極限定理 | zh_TW |
| dc.title | Central Limit Theorem for Linear Eigenvalue Statistics of Generalized Wigner Matrices | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 許順吉,姜祖恕 | |
| dc.subject.keyword | 隨機矩陣,特徵值,中央極限定理, | zh_TW |
| dc.subject.keyword | Random matrices,,Eigenvalues,Central limit theorem, | en |
| dc.relation.page | 32 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2012-07-10 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-101-1.pdf | 328.33 kB | Adobe PDF | 檢視/開啟 |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。