|
植田 優基
ウエダ ユウキ UEDA Yuki 所 属 旭川校 職 名 准教授 |
|
| 言語種別 | 日本語 |
| 発行・発表の年月 | 2026/05 |
| 形態種別 | 学術雑誌 |
| 査読 | 査読あり |
| 標題 | Monotone max-convolution and subordination functions for free max-convolution |
| 執筆形態 | 単著 |
| 掲載誌名 | Annales Mathématiques Blaise Pascal |
| 掲載区分 | 国外 |
| 総ページ数 | 17 |
| 担当区分 | 筆頭著者 |
| 著者・共著者 | Yuki Ueda |
| 概要 | We show that the distribution of the spectral maximum of monotonically independent self-adjoint operators coincides with the classical max-convolution of their distributions. In free probability, it was proven that for any probability measures $\sigma,\mu$ on $\mathbb{R}$ there is a unique probability measure $\mathbb{A}_\sigma(\mu)$ satisfying $\sigma\boxplus \mu = \sigma \triangleright \mathbb{A}_\sigma(\mu)$, where $\boxplus$ and $\triangleright$ are free and monotone additive convolutions, respectively. We recall that the reciprocal Cauchy transform of $\mathbb{A}_\sigma(\mu)$ is the subordination function for free additive convolution. Motivated by this analogy, we introduce subordination functions for free max-convolution and prove their existence and structural properties. |