分数自由卷积幂

IF 1.2 2区数学 Q1 MATHEMATICS

Indiana University Mathematics Journal Pub Date : 2020-09-03 DOI:10.1512/iumj.2022.71.9163

D. Shlyakhtenko, Terence Tao. With an appendix by David Jekel

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引用次数: 20

摘要

Bercovici-Voiculescu和Nica-Speicher将自由卷积幂的概念推广$k \mapsto \mu^{\boxplus k}$到非整数$k \geq 1$的情况，并与随机矩阵理论中的次要过程有关。本文给出了这一连续环境下自由熵和(归一化)自由卷积幂的自由Fisher信息的单调性的两个证明，并建立了这一过程的一个有趣的变分描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fractional free convolution powers

The extension $k \mapsto \mu^{\boxplus k}$ of the concept of a free convolution power to the case of non-integer $k \geq 1$ was introduced by Bercovici-Voiculescu and Nica-Speicher, and related to the minor process in random matrix theory. In this paper we give two proofs of the monotonicity of the free entropy and free Fisher information of the (normalized) free convolution power in this continuous setting, and also establish an intriguing variational description of this process.

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来源期刊

Indiana University Mathematics Journal 数学-数学

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

4.5 months

期刊介绍： Information not localized