论文标题
关于非线性随机矩阵模型的均匀动力学方程的推导
On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model
论文作者
论文摘要
我们考虑了一个非线性ODES系统，其中基础线性动力学由Hermitian随机矩阵集合确定。我们证明，弱非线性，无限体积限制中的领先顺序动力学是通过对非平整时间尺度上相应动力学方程的解决方案确定的。我们的证明依赖于从Weingarten微积分获得的HAAR分布的统一矩阵的估计，这可能具有独立的利益。
We consider a nonlinear system of ODEs, where the underlying linear dynamics are determined by a Hermitian random matrix ensemble. We prove that the leading order dynamics in the weakly nonlinear, infinite volume limit are determined by a solution to the corresponding kinetic wave equation on a non-trivial timescale. Our proof relies on estimates for Haar-distributed unitary matrices obtained from Weingarten calculus, which may be of independent interest.
