Random Matrices, Complexity and Slow Dynamics in Random Media

无序和随机性会导致系统非常复杂。这个项目研究的重要性，这种诱导的复杂性的时间演化的系统。因此，它解决了数学和统计物理学之间的界面无序介质的主题。这些复杂系统的动力学的复杂性的签名被认为是在事实上，进化是非常缓慢的，并被困在远离平衡的区域。它表现出老化等新的特征，打破了早已确立的波动-耗散规律。然而，这些复杂的系统有一些共同的特征，这个项目为理解这些普遍现象奠定了基础。这种普遍的行为表现在非常不同的模型，其中包括自旋玻璃的慢动力学，无论是球形和伊辛自旋，和无序结构，如渗滤集群和随机树的扩散和运输。最近建立的工具之一（由PI）是随机能量景观和随机矩阵理论研究之间的一个新的和强大的联系。这种联系也将进一步探讨，因为它使一个新的分类的不同类别的复杂行为的一类系统（球面自旋玻璃）的介绍。

Disorder and randomness can induce very deep complexity for systems. This project studies the importance of this induced complexity on the time evolution of such systems. It thus addresses topics at the interface between mathematics and statistical physics of disordered media. The signature of complexity on the dynamics of these complex systems is seen in the fact that the evolution is very slow and trapped in regions far from equilibrium. It exhibits new characteristics like aging, and break the well established rules of fluctuation-dissipation. Nevertheless some universal features are shared by these complex systems and this project builds the foundations for understanding these universal phenomena. This universal behavior is exhibited in very different models which include the slow dynamics of Spin glasses, both for spherical and Ising spins, and the diffusion and transport on disordered structures like percolation clusters and random trees. One of the tools recently built (by the PI) is a new and powerful link between the study of the random energy landscapes and random matrix theory. This link will also be explored further since it enables the introduction of a new classification of different classes of complex behavior in one class of systems (the spherical spin glasses).