论文标题
自由独立的硬币折腾，标准的年轻Tableaux和Kesten--McKay Law
Freely Independent Coin Tosses, Standard Young Tableaux, and the Kesten--McKay Law
论文作者
论文摘要
在本文中，我们将从$ d $的普通树上进行封闭的步行。这些步道由Kesten-McKay Law描述为$ n $顶点上随机$ d $ regartar图的渐近分布。我们将证明，Kesten-McKay Law的时刻是通过将标准的年轻Tableaux计入最多2行来给出的，即使$ d $不是整数，步行的某些属性也有意义。我们将使用自由概率指导我们如何在随机矩阵理论中构建明确的模型。
In this article, we shall start with a closed walk on a regular tree of degree $d$. These walks are described by the Kesten-McKay law which arises as the asymptotic distribution of a random $d$-regular graph on $n$ vertices. We will show that the moments of the Kesten-McKay law are given by counting standard Young tableaux with at most 2 rows, and how some properties of the walk make sense even when $d$ is not an integer. We will use free probability to instruct us how to build an explicit model in random matrix theory.
