论文标题
Hermitian随机矩阵的乘法统计数据和全差异painlevéII方程的通用性
Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation
论文作者
论文摘要
我们研究了单位不变的Hermitian随机矩阵模型的特征值的乘法统计。我们考虑一个切割的常规多项式势和一类大量的乘法统计。我们表明，在大型矩阵中，几个相关量会收敛到所考虑的乘法统计的潜力和家族中普遍存在的限制。反过来，这种通用限制是由界面分化的PainlevéIE方程来描述的，尤其是它们在任何有限的时间将所考虑的随机矩阵模型与KPZ方程相关联。
We study multiplicative statistics for the eigenvalues of unitarily-invariant Hermitian random matrix models. We consider one-cut regular polynomial potentials and a large class of multiplicative statistics. We show that in the large matrix limit several associated quantities converge to limits which are universal in both the potential and the family of multiplicative statistics considered. In turn, such universal limits are described by the integro-differential Painlevé II equation, and in particular they connect the random matrix models considered with the narrow wedge solution to the KPZ equation at any finite time.
