The local universality of Muttalib–Borodin biorthogonal ensembles with parameter θ=12
The local universality of Muttalib–Borodin biorthogonal ensembles with parameter θ=12
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DOI：
10.1088/1361-6544/ab247c
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发表时间：
2018-10
期刊：
影响因子：
1.7
通讯作者：
A. Kuijlaars;L. Molag
中科院分区：
文献类型：
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作者：
A. Kuijlaars;L. Molag
Muttalib-Borodin 双正交系综是正实线上 n 个粒子的概率密度函数，取决于参数和外场。因为我们发现相关相关核的大 n 行为对 仅有很少的限制。这个想法是将系综与 II 型多重正交多项式系综联系起来，而后者又可以与黎曼-希尔伯特问题相关，然后我们用 Deift-Zhou 最速下降法来解决该问题。主要成分是借助 Meijer G 函数在原点构建局部参数矩阵，及其与全局参数矩阵的匹配条件。我们将提出一种新的迭代技术来获取匹配条件，我们希望该技术也适用于更一般的情况。
The Muttalib–Borodin biorthogonal ensemble is a probability density function for n particles on the positive real line that depends on a parameter and an external field . For we find the large n behavior of the associated correlation kernel with only few restrictions on . The idea is to relate the ensemble to a type II multiple orthogonal polynomial ensemble that can in turn be related to a Riemann–Hilbert problem which we then solve with the Deift–Zhou steepest descent method. The main ingredient is the construction of the local parametrix at the origin, with the help of Meijer G-functions, and its matching condition with a global parametrix. We will present a new iterative technique to obtain the matching condition, which we expect to be applicable in more general situations as well.