隨機多項式臨界點之大離差行為

Large deviations for critical points of random polynomials

吳逸安(Yi-An Wu)

指導教授 ： 張志中

國立臺灣大學/理學院/應用數學科學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201701979

摘要

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。

關鍵字

隨機多項式 ； 大離差 ； 臨界點 ； Levy 距離 ； 機率測度空間

並列摘要

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.

並列關鍵字

random polynomial ； large deviation ； critical point ； Lévy distance ； space of probability measure

參考文獻

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