具有Fisher-Hartwig奇性的Muttalib-Borodin行列式的渐近性
Asymptotics of Muttalib-Borodin determinants with Fisher-Hartwig singularities
摘要：
Muttalib-Borodin行列式是Hankel行列式的推广，它依赖于参数$θ>0$ .本文得到了权具有任意多个Fisher-Hartwig奇点的$n \times n$ Muttalib-Borodin行列式的大$n$渐近性.作为推论，我们得到的期望和方差的实部和虚部的对数的特征多项式，几个中心极限定理，和一些全球性的体积刚度上界的渐近。我们的结果对所有的$θ> 0$都是有效的。
英文摘要：
Muttalib-Borodin determinants are generalizations of Hankel determinants and depend on a parameter $θ>0$. In this paper, we obtain large $n$ asymptotics for $n \times n$ Muttalib-Borodin determinants whose weight possesses an arbitrary number of Fisher-Hartwig singularities. As a corollary, we obtain asymptotics for the expectation and variance of the real and imaginary parts of the logarithm of the characteristic polynomial, several central limit theorems, and some global bulk rigidity upper bounds. Our results are valid for all $θ> 0$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
