论文标题
当参数$θ$是整数的倒数时，muttalib-borodin的本地普遍性
The local universality of Muttalib-Borodin ensembles when the parameter $θ$ is the reciprocal of an integer
论文作者
论文摘要
muttalib-borodin集合是正面真实轴上$ n $粒子的概率密度函数，取决于参数$θ$和权重$ w $。我们考虑一个取决于外部场$ V $的不同指数重量。在最近的一篇文章中，发现了硬边缘的相关关联内核的大$ n $行为，以$θ= \ frac {1} {2} $，在$ v $上只施加了少数限制。在当前文章中，我们概括了本文的技术和结果，以获得$θ= \ frac {1} {r} $的类似结果，其中$ r $是一个正整数。该方法是将合奏与II型多个正交多项式合奏与$ r $ $ strize联系起来，然后可以与$（r+1）\ times（r+1）$ riemann-hilbert问题有关。原点周围的本地参数是使用Meijer G功能构建的。我们将围绕原点的本地参数与全局参数匹配，并具有双匹配，这是最近引入的这项技术。
The Muttalib-Borodin ensemble is a probability density function for $n$ particles on the positive real axis that depends on a parameter $θ$ and a weight $w$. We consider a varying exponential weight that depends on an external field $V$. In a recent article, the large $n$ behavior of the associated correlation kernel at the hard edge was found for $θ=\frac{1}{2}$, where only few restrictions are imposed on $V$. In the current article we generalize the techniques and results of this article to obtain analogous results for $θ=\frac{1}{r}$, where $r$ is a positive integer. The approach is to relate the ensemble to a type II multiple orthogonal polynomial ensemble with $r$ weights, which can then be related to an $(r+1)\times (r+1)$ Riemann-Hilbert problem. The local parametrix around the origin is constructed using Meijer G-functions. We match the local parametrix around the origin with the global parametrix with a double matching, a technique that was recently introduced.
