Statistical mechanics of complex systems

在这个项目中，我们将使用统计物理学的工具和思想来研究理论生态学、数学生物学和进化动力学等领域的复杂系统模型。我们将研究的一个初始问题是具有分区相互作用结构的复杂生态系统的稳定性。我们会问这样一个系统的什么特征使均衡分别稳定或不稳定。为了做到这一点，我们将使用无序系统统计物理中的技术，特别是随机矩阵理论，自旋玻璃物理中的生成泛函方法和数值模拟。新的物理科学内容在于这些数学方法的进一步发展，以及它们对理论生态学和其他学科中长期存在的问题的应用。

In this project we will use tools and ideas from statistical physics to study complex systems models in fields such as theoretical ecology,mathematical biology, and evolutionary dynamics. One initial question we will study concerns the stability of complex ecosystems with compartmented interaction structures. We will ask what features of such a system make equilibria stable or unstable respectively. To do this we will use techniques from the statistical physics of disordered systems, in particular random-matrix theory, generating-functional methods from spin glass physics, and numerical simulations. The novel physical sciences content consists in the further development of these mathematical methods, and their application to long-standing problems in theoretical ecology and other disciplines.