论文标题
大型动力学随机矩阵模型的艾科尼尔公式
Eikonal formulation of large dynamical random matrix models
论文作者
论文摘要
动态随机矩阵模型的标准方法取决于特征值轨迹的描述。使用来自光学的类比，基于Fermat原理（轨迹）和Huygens原理（Wavefronts）之间的二元性，我们为大型随机矩阵模型制定了汉密尔顿 - 雅各布动力学。结果方程式以统一的方式描述了一类广泛的随机矩阵模型，包括正常（遗传学或单一）以及严格的非正常动力学。 HJ形式主义适用于布朗桥动力学，可以计算Harish-Chandra-Itzykson-Zuber积分的渐近学。
Standard approach to dynamical random matrix models relies on the description of trajectories of eigenvalues. Using the analogy from optics, based on the duality between the Fermat principle(trajectories) and the Huygens principle (wavefronts), we formulate the Hamilton-Jacobi dynamics for large random matrix models. The resulting equations describe a broad class of random matrix models in a unified way, including normal (Hermitian or unitary) as well as strictly non-normal dynamics. HJ formalism applied to Brownian bridge dynamics allows one for calculations of the asymptotics of the Harish-Chandra-Itzykson-Zuber integrals.
