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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/2584完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張志中 | |
| dc.contributor.author | I-Shing Hu | en |
| dc.contributor.author | 胡亦行 | zh_TW |
| dc.date.accessioned | 2021-05-13T06:42:32Z | - |
| dc.date.available | 2017-02-17 | |
| dc.date.available | 2021-05-13T06:42:32Z | - |
| dc.date.copyright | 2017-02-17 | |
| dc.date.issued | 2017 | |
| dc.date.submitted | 2017-02-15 | |
| dc.identifier.citation | Sean O'Rourke, Critical points of random polynomials
and characteristic polynomials of random matrices. arXiv: 1412.4703v1 (2014). T. R. R. Annapareddy, On critical points of random polynomials and spectrum of certain products of random matrices. arXiv: 1602.05298v1 (2016) R. Pemantle and I. Rivin, The distribution of zeros of the derivative of a random polynomial}. Advances in Combinatorics, Springer (2013), pp. 259 -- 273. arXiv:1109.5975. Z. Kabluchko, Critical points of random polynomials with independent identically distributed roots}. Proc. Amer. Math. Soc. 143 (2015), no. 2, pp. 695 -- 702. arXiv: 1206.6692v2. P. L. Cheung, T. W. Ng, J. Tsai,and S. C. P. Yam, Higher order, polar and Sz.-Nagy's generalized derivatives of random polynomials with independent and identically distributed zeros on the unit circle. Computational Methods and Function Theory (2014), pp. 1 -- 28. Z. Kabluchko and D. Zaporozhets, Asymptotic distribution of complex zeros of random analytic functions. Ann. Probab., 42 (4) (2014), pp. 1374 -- 1395. G. W. Anderson,A. Guionnet, and O. Zeitouni, An introduction to random matrices. Cambridge studies in advanced mathematics. Cambridge University Press, 2009. Z. D. Bai and J. W. Silverstein, Spectral analysis of large dimensional random matrices. 2nd edition, Springer, 2010. A. Lytova and L. Pastur, Central limit theorem for linear eigenvalue statistics of random matrices with independent entries. Ann. Probab. (2009), pp. 1778-1840. A. Lytova and L. Pastur, Non-Gaussian limiting laws for the entries of regular functions of the Wigner matrices. arXiv: 1103.2345v2 (2011) Z. D. Bai, X. Y. Wang, and W. Zhou, CLT for linear spectral statistics of Wigner matrices. Electronic Journal of Probab. vol 14 (2009) pp. 2391 -- 2417. I. Jana, K. Saha, and A. Soshnikov, extit{Fluctuations of linear eigenvalue statistics of random band matrices}. arXiv: 1412.2445v2 (2015) L. Y. Li, M. Reed, and A. Soshnikov, Central limit theorem for linear eigenvalue statistics for submatrices of Wigner random matrices. arXiv: 1504.05933v1 (2015) Phil Kopel, Regularity conditions for convergence of linear statistics of GUE. arXiv: 1510.02988v2 (2015) P. Sosoe and P. Wong, Regularity conditions in the CLT for linear eigenvalue statistics of Wigner matrices. arXiv: 1210.5666v2 (2015) W. S. Cheung and T. W. Ng, A companion matrix approach to the study of zeros and critical points of a polynomial. J. Math. Anal. Appl. 319 (2006), no. 2, pp. 690 -- 707. N. G. de Bruijn and T. A. Springer, On the zeros of a polynomial and of its derivative II. Indag. Math. 9 (1947), pp. 264 -- 270. P. Erdos and I. Niven, On the roots of a polynomial and its derivative. Bull Amer. Math. Soc. 54 (1948), pp. 184 -- 190. A. T. Bharucha-Reid and M. Sambandham, Random Polynomials. Probability and Mathematical Statistics: a Series of Monographs and Textbooks. Academic Press, 1986. V. I. Bogachev, Measure Theory. Vol II}. Springer, 2007. The common limit of the linear statistics of zeros of random polynomials and their derivatives II. In preparation (2017) | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/2584 | - |
| dc.description.abstract | Let $ p_n(x) $ be a random polynomial of degree $n$ and
${Z^{(n)}_j}_{j=1}^n$ and ${X^{n, k}_j}_{j=1}^{n-k}, k<n$, be the zeros of $p_n$ and $p_n^{(k)}$, the $k$th derivative of $p_n$, respectively. We show that if the linear statistics $displaystyle{ %L_n (f) &=& frac {1}{a_n} left[ fleft( frac {Z^{(n)}_1}{b_n} ight) + cdots + f left(frac {Z^{(n)}_n}{b_n} ight) ight]}$ associated with ${Z^{(n)}_j}$ has a limit as $n oinfty$ at some mode of convergence, the linear statistics associated with ${X^{n, k}_j}$ converges to the same limit at the same mode. Similar statement also holds for the centered linear statistics associated with the zeros of $p_n$ and $p_n^{(k)}$, provided the zeros ${Z^{(n)}_j}$ and the sequences ${a_n}$ and ${b_n}$ of positive numbers satisfy some mild conditions. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-13T06:42:32Z (GMT). No. of bitstreams: 1 ntu-106-R02221015-1.pdf: 1014409 bytes, checksum: 20debac55d3540792e661ca4850e0841 (MD5) Previous issue date: 2017 | en |
| dc.description.tableofcontents | 口試委員會審定書……………………………………………………...……………
誌謝………………………………………………………………..………………….ii 英文摘要………………………………………………………...…………….…….iii Introduction………………………………………………………….………………..1 A Comparison Identity………………………………………………………………..6 Proofs and Concluding Remarks……………………………………………………...8 Large Deviations………………………...…………………………………………..10 Appendix…………………………………………………………………………….12 Reference…………………………………………………………………….…...… 17 | |
| dc.language.iso | en | |
| dc.subject | 普遍性 | zh_TW |
| dc.subject | 隨機多項式 | zh_TW |
| dc.subject | 隨機矩陣 | zh_TW |
| dc.subject | random matrices | en |
| dc.subject | random polynomials | en |
| dc.subject | universality | en |
| dc.title | 隨機多項式的一個普遍性 | zh_TW |
| dc.title | A Universality of Polynomials with Complex Random Roots | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 105-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳宏,黃啟瑞,江金倉 | |
| dc.subject.keyword | 隨機多項式,隨機矩陣,普遍性, | zh_TW |
| dc.subject.keyword | random polynomials,random matrices,universality, | en |
| dc.relation.page | 18 | |
| dc.identifier.doi | 10.6342/NTU201700594 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2017-02-15 | |
| 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 | |
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