论文标题
与循环jacobi $β$增强的渐近相关性
Asymptotic correlations with corrections for the circular Jacobi $β$-ensemble
论文作者
论文摘要
先前的工作已经考虑了针对经典随机矩阵集成的各种相关函数的缩放限制的领先校正项及其在硬和软边缘处的$β$概括。已经发现，该校正的功能形式是通过应用于领先项的导数操作给出的。在目前的工作中，我们计算了具有dyson Indices $β= 1,2 $和4的圆形雅各比集合的相关内核的领先校正项，并在相应的$β$中均以$β$均匀地结合。前者需要进行涉及Routh-Romanovski多项式的分析，而后者基于基于插孔多项式的广义超几何序列的多维积分公式。在所有情况下，都发现该校正项与导数操作有关。
Previous works have considered the leading correction term to the scaled limit of various correlation functions and distributions for classical random matrix ensembles and their $β$ generalisations at the hard and soft edge. It has been found that the functional form of this correction is given by a derivative operation applied to the leading term. In the present work we compute the leading correction term of the correlation kernel at the spectrum singularity for the circular Jacobi ensemble with Dyson indices $β= 1,2$ and 4, and also to the spectral density in the corresponding $β$-ensemble with $β$ even. The former requires an analysis involving the Routh-Romanovski polynomials, while the latter is based on multidimensional integral formulas for generalised hypergeometric series based on Jack polynomials. In all cases this correction term is found to be related to the leading term by a derivative operation.
