Statistical mechanics of complex systems

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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.