分数阶自由卷积幂
Fractional free convolution powers
摘要：
自由卷积幂的概念到非整数$k \geq 1$的情况的扩展$k \mapsto μ^{\boxplus k}$是由Bercovici-Voiculescu和Nica-Speicher引入的，并且与随机矩阵理论中的子过程有关。在本文中，我们给出了两个证明的单调性的自由熵和自由Fisher信息的（归一化）的自由卷积功率在这个连续设置，也建立了一个有趣的变分描述这个过程。
英文摘要：
The extension $k \mapsto μ^{\boxplus k}$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
