Mathematical Sciences: Structure Function Asymptotics for Correlated Random Fields and Networks

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The project will investigate various properties of random networks and random fields indexed by graphs. A number of long range properties of stochastic processes are closely related with the natural orderings of the indexing set. Indexing by graphs, along with the imposed dependence structure on the process result in many diverse interesting properties such as phase transition, symmetry breakdowns, and chaotic behaviors at infinity. The resulting models find applications in cellular automata, neural networks, magnetic and electrical properties of materials, socio- economic planning etc.