论文标题
通过多项式的根源自由卷积能力
Free Convolution Powers via Roots of Polynomials
论文作者
论文摘要
令$μ$为真实线上的紧凑型概率度量。 Bercovici-Voiculescu和Nica-Speicher证明了任何真正的$ k \ geq 1 $的自由卷积功率$μ^{\ boxplus k} $。此简短说明的目的是在多项式和根部的衍生物中给出$μ^{\ boxplus k} $的基本描述。这座桥使我们能够在自由概率和多项式的渐近行为之间来回切换。
Let $μ$ be a compactly supported probability measure on the real line. Bercovici-Voiculescu and Nica-Speicher proved the existence of a free convolution power $μ^{\boxplus k}$ for any real $k \geq 1$. The purpose of this short note is to give an elementary description of $μ^{\boxplus k}$ in terms of of polynomials and roots of their derivatives. This bridge allows us to switch back and forth between free probability and the asymptotic behavior of polynomials.
