Large Gap Asymptotics at the Hard Edge for Product Random Matrices and Muttalib-Borodin Ensembles
Large Gap Asymptotics at the Hard Edge for Product Random Matrices and Muttalib-Borodin Ensembles
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DOI：
10.1093/imrn/rnx202
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发表时间：
2019-05-01
影响因子：
1
通讯作者：
Stivigny, Dries
中科院分区：
文献类型：
--
作者：
Claeys, Tom;Girotti, Manuela;Stivigny, Dries
本文研究了一类正定Hermite随机矩阵的最小特征值的分布。它们的极限分布可以表示为与Meijer G-函数或Wright广义贝塞尔函数构建的核相关联的积分算子的Fredholm行列式。它们以自然的方式推广了硬边贝塞尔核Fredholm行列式。我们表示的Fredholm行列式的对数导数相同的2x2 Riemann-Hilbert问题，并使用这种表示，以获得所谓的大间隙渐近。
We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large. Their limit distributions can be expressed as Fredholm determinants of integral operators associated to kernels built out of Meijer G-functions or Wright's generalized Bessel functions. They generalize in a natural way the hard edge Bessel kernel Fredholm determinant. We express the logarithmic derivatives of the Fredholm determinants identically in terms of a 2x2 Riemann-Hilbert problem, and use this representation to obtain the so-called large gap asymptotics.