论文标题
多切割措施的自由添加卷积的支持
The support of the free additive convolution of multi-cut measures
论文作者
论文摘要
We consider the free additive convolution $μ_α\boxplusμ_β$ of two probability measures $μ_α$ and $μ_β$, supported on respectively $n_α$ and $n_β$ disjoint bounded intervals on the real line, and derive a lower bound and an upper bound that is strictly smaller than $2n_αn_β$, on the number of connected components in its support.我们还获得了免费的添加卷积半组$ \ {μ^{\ boxplus t} \，：\，t \ ge 1 \} $的相应结果。在整个论文中，我们考虑使用功率法行为的概率措施的类别在其支持的终点，指数从$ -1 $到$ 1 $不等。我们的主要定理将BAO，ERDőS和Schnelli〜 [4]的结果概括为多切割设置。
We consider the free additive convolution $μ_α\boxplusμ_β$ of two probability measures $μ_α$ and $μ_β$, supported on respectively $n_α$ and $n_β$ disjoint bounded intervals on the real line, and derive a lower bound and an upper bound that is strictly smaller than $2n_αn_β$, on the number of connected components in its support. We also obtain the corresponding results for the free additive convolution semi-group $\{μ^{\boxplus t}\,:\, t\ge 1\}$. Throughout the paper, we consider classes of probability measures with power law behaviors at the endpoints of their supports with exponents ranging from $-1$ to $1$. Our main theorem generalizes a result of Bao, Erdős and Schnelli~[4] to the multi-cut setup.
