论文标题
自由添加量卷积的密度多切割度量
Density of the free additive convolution of multi-cut measures
论文作者
论文摘要
我们考虑免费的添加卷积半群$ \lbraceμ^{\ boxplus t}：\，t \ ge 1 \ rbrace $，并确定$μ^{\ boxplus t} $的局部行为在端口和支持的任何端点。然后，我们研究了两种多切割概率度量的自由添加卷积，并表明其密度在其支撑的任何端点上都是平方根或立方根的衰减。本文考虑的概率措施满足了权力法行为，指数严格在$ -1 $至1美元之间，在其支持的端点上。
We consider the free additive convolution semigroup $\lbrace μ^{\boxplus t}:\,t\ge 1\rbrace$ and determine the local behavior of the density of $μ^{\boxplus t}$ at the endpoints and at any singular point of its support. We then study the free additive convolution of two multi-cut probability measures and show that its density decays either as a square root or as a cubic root at any endpoints of its support. The probability measures considered in this paper satisfy a power law behavior with exponents strictly between $-1$ and $1$ at the endpoints of their supports.
