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

该项目将研究随机网络和由图索引的随机场的各种性质。随机过程的许多长程性质与指数集的自然序密切相关。图的索引以及对过程施加的依赖结构导致了许多有趣的性质，如相变、对称性破缺和无穷远处的混沌行为。由此产生的模型在细胞自动机、神经网络、材料的磁电性质、社会经济规划等方面得到了应用。

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.