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植田 優基
ウエダ ユウキ UEDA Yuki 所 属 旭川校 職 名 講師 |
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| 発表年月日 | 2024/10 |
| 発表テーマ | The limiting behavior of empirical root distributions of polynomials and application to free probability |
| 会議名 | Non-Commutative Probability and Related Topics 2024 |
| 発表区分 | 学会発表 |
| 発表形式 | 口頭（一般） |
| 単独共同区分 | 単独 |
| 開催期間 | 2024/10/16～2024/10/18 |
| 種別 | 国際的又は全国的規模 |
| 発表者・共同発表者 | 植田 優基 |
| 概要 | We characterize the limiting behavior of empirical root distributions (ERD) of positive real-
rooted polynomials via some methods of free probability. Roughly speaking, we prove that the weak convergence of ERD of polynomials holds if and only if the ratio of consecutive coefficients of polynomials converges to Voiculescu’s S-transform of the limiting measure when their degree tends to infinity. Thanks to our result, we can observe rich relationships between free probability and theory of polynomial convolutions. This is a joint work with Octavio Arizmendi (CIMAT), Katsunori Fujie (Kyoto University) and Daniel Perales (Texas A&M). |