Statistical physics approaches to complex systems
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This thesis utilizes statistical physics concepts and mathematical modeling to study complex systems. I investigate the emergent complexities in two systems: (i) the stock volume volatility in the United States stock market system; (ii) the robustness of networks in an interdependent lattice network system. In Part I, I analyze the United States stock market data to identify how several financial factors significantly affect scaling properties of volume volatility time intervals. I study the daily trading volume volatility time intervals between two successive volume volatilities above a certain threshold q, and find a range of power law distributions. I also study the relations between the form of these distribution functions and several financial factors: stock lifetimes, market capitalization, volume, and trading value. I find that volume volatility time intervals are short-term correlated. I also find that the daily volume volatility shows a stronger long-term correlation for sequences of longer lifetimes. In Part II, I apply percolation theory to interacting complex networks. The dependency links between the two square lattice networks have a typical length r lattice units. For two nodes connecting by a dependency link, one node fails once the node on which it depends in the other network fails. I show that rich phase transition phenomena exist when the length of the dependency links r changes. The results suggest that percolation for small r is a second-order transition, and for larger r is a first-order transition. The study suggests that interdependent infrastructures embedded in two-dimensional space become most vulnerable when the interdependent distance is in the intermediate range, which is much smaller than the size of the system.