论文标题
分数自由卷积能力
Fractional free convolution powers
论文作者
论文摘要
Bercovici-voiculescu和Nica-Speicher引入了扩展$ k \mapstoμ^{\ boxplus k} $ to non-Integer $ k \ geq 1 $的概念的概念，并与随机矩阵理论中的次要过程有关。在本文中，我们给出了两个证据，证明了在这种连续环境中（归一化）自由卷积能力的自由熵和自由渔民信息，并为此过程建立了有趣的变化描述。
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.
