论文标题
Laguerre单一合奏的最大特征值分布的渐近学
Asymptotics of the Largest Eigenvalue Distribution of the Laguerre Unitary Ensemble
论文作者
论文摘要
我们研究了$ n \ times n $ hermitian矩阵的所有特征值，从laguerre单一合奏带有$ x^γ\ mathrm {e}^{ - 4nx}，\ x \ in [0，\ iftty），\;γ> -1 $ $ [0，通过使用以前的结果来获得正交多项式的梯子运算符获得的有限$ n $，我们得出了最大的特征值分布功能的大$ n $渐近器，$α$从0到柔软的边缘。另外，在软边，我们计算了Tracy和widom [Commun。数学。物理。 159（1994），151-174]，后来由Deift和Krasovsky [Commun。数学。物理。 278（2008），643-678]。我们的结果降低为Deift等人的结果。当$γ= 0 $。
We study the probability that all the eigenvalues of $n\times n$ Hermitian matrices, from the Laguerre unitary ensemble with the weight $x^γ\mathrm{e}^{-4nx},\;x\in[0,\infty),\;γ>-1$, lie in the interval $[0,α]$. By using previous results for finite $n$ obtained by the ladder operator approach of orthogonal polynomials, we derive the large $n$ asymptotics of the largest eigenvalue distribution function with $α$ ranging from 0 to the soft edge. In addition, at the soft edge, we compute the constant conjectured by Tracy and Widom [Commun. Math. Phys. 159 (1994), 151-174], later proved by Deift, Its and Krasovsky [Commun. Math. Phys. 278 (2008), 643-678]. Our results are reduced to those of Deift et al. when $γ=0$.
