Hermite随机矩阵乘性统计量的普适性与积分微分Painlevé II方程
Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation
摘要：
研究酉不变Hermite随机矩阵模型特征值的乘性统计量。我们考虑一次切割正规多项式的潜力和一大类乘法统计。我们表明，在大矩阵的限制，几个相关的数量收敛到限制，这是普遍的潜力和家庭的乘法统计考虑。反过来，这样的普遍限制描述的积分微分Painlevé II方程，特别是他们连接随机矩阵模型考虑与窄楔形解决方案的KPZ方程在任何有限的时间。
英文摘要：
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.
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