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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/67717完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張志中 | |
| dc.contributor.author | Yi-An Wu | en |
| dc.contributor.author | 吳逸安 | zh_TW |
| dc.date.accessioned | 2021-06-17T01:45:50Z | - |
| dc.date.available | 2017-07-28 | |
| dc.date.copyright | 2017-07-28 | |
| dc.date.issued | 2017 | |
| dc.date.submitted | 2017-07-26 | |
| dc.identifier.citation | [1] R. Pemantle, I. Rivin, The distribution of zeros of the derivative of a random polynomial,Advances in Combinatorics. Waterloo Workshop in Computer Algebra 2011,I. Kotsireas and E. V. Zima, editors, Springer, New York, 2013.
[2] Z. Kabluchko, Critical points of random polynomials with independent identically distributed roots. arXiv:1206.6692v2 (2012). [3] Sean O’Rourke, Critical points of random polynomials and characteristic polynomials of random matrices. arXiv:1412.4703v1 (2014). [4] F. Rassoul-Agha and T. Seppäläinen, A course on large deviations with an introduction to Gibbs measures. Graduate Studies in Mathematics, 162, American Mathematical Society, Providence, 2015. [5] S. Ghosh and O. Zeitouni, Large deviations for zeros of random polynomials with i.i.d. exponential coefficients. arXiv:1312.6195v4 (2015). [6] A. Guionnet, Large Random Matrices: Lectures on Macroscopic Asymptotics. Springer, 2009. [7] I. S. Hu and C. C. Chang, The Common Limit of the Linear Statistics of Zeros of Random Polynomials and Their Derivatives. arXiv:1701.03946 (2017). [8] O. van Gaans, Probability measures on metric spaces. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/67717 | - |
| dc.description.abstract | 設pn 為一n 次隨機多項式，若pn 之根所形成的測度其分布滿足大離差行為，我們證明在一些情形下，pn 之臨界點所形成的測度其分布亦滿足相同之大離差行為。 | zh_TW |
| dc.description.abstract | Let pn be a random polynomial with degree n. If the distributions of the empirical measure of zeros of pn satisfy large deviation principle, we show that the distributions of the empirical measure of critical points of pn satisfy the same large deviation principle in some special cases. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T01:45:50Z (GMT). No. of bitstreams: 1 ntu-106-R02246015-1.pdf: 360338 bytes, checksum: 0daba0472d2e6acaef4935954d7788c7 (MD5) Previous issue date: 2017 | en |
| dc.description.tableofcontents | 口試委員會審定書i
摘要ii Abstract iii 1 Introduction 1 2 Large deviations for critical points of random polynomials with real zeros 6 A Weak topology of probability measures 12 B Basic notions of large deviations 17 C Relative entropy 21 D Sanov’s theorem 25 Bibliography 33 | |
| dc.language.iso | en | |
| dc.subject | 隨機多項式 | zh_TW |
| dc.subject | 大離差 | zh_TW |
| dc.subject | 臨界點 | zh_TW |
| dc.subject | Levy 距離 | zh_TW |
| dc.subject | 機率測度空間 | zh_TW |
| dc.subject | large deviation | en |
| dc.subject | random polynomial | en |
| dc.subject | space of probability measure | en |
| dc.subject | Levy distance | en |
| dc.subject | critical point | en |
| dc.title | 隨機多項式臨界點之大離差行為 | zh_TW |
| dc.title | Large deviations for critical points of random polynomials | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 105-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳宏,黃啟瑞 | |
| dc.subject.keyword | 隨機多項式,大離差,臨界點,Levy 距離,機率測度空間, | zh_TW |
| dc.subject.keyword | random polynomial,large deviation,critical point,Levy distance,space of probability measure, | en |
| dc.relation.page | 33 | |
| dc.identifier.doi | 10.6342/NTU201701979 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2017-07-27 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
| 顯示於系所單位： | 應用數學科學研究所 | |
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