Stability and Complexity: New insights from Random Matrix Theory

复杂性是自然规律：大型生态系统、人脑和湍急的流体只是复杂系统的几个例子。本项目旨在研究和分类基于普适概率模型的大型复杂系统的稳定性判据。这个项目期望利用随机矩阵理论中的尖端技术来产生对稳定性的新的重要理解。该项目的预期成果包括发展和扩大一个创新的数学框架和技术，以便对大型复杂系统的稳定性问题采取统一和普遍的办法。

Complexity is a rule of nature: large ecosystems, the human brain, and turbulent fluids are merely a few examples of complex systems. This project aims to study and classify criteria of stability in large complex systems based on universal probabilistic models. This project expects to generate new important understanding of stability using cutting-edge techniques from random matrix theory. Expected outcomes of this project include development and expansion of an innovative mathematical framework and techniques which allow a unified and universal approach to the question of stability in large complex systems.