Mathematical Sciences: Studies in Interacting Particle Systems

该项目将支持对概率论中若干问题的研究。Liggett将考虑与相互作用粒子系统相关的几个问题：随机环境中接触过程的生存和灭绝，排斥过程中收敛到平衡的速度，阈值选民模型的生存，以及无穷序列队列的极限行为。Schonmann将考虑相互作用粒子系统和大偏差中的问题：随机Ising模型的亚稳态、元胞自动机的临界行为和随机场的大偏差。主要研究人员将对概率论中的几个问题进行研究。主要的焦点将放在粒子的相互作用系统上。这些系统出现在物理和生物系统的建模中，并在其他领域有应用，比如计算机科学。

The project will support research into a number of problems in probability theory. Liggett will consider several questions related to interacting particle systems: survival and extinction of contact processes in random environments, rates of convergence to equilibrium in the exclusion process, survival of the threshold voter model, and the limiting behavior of an infinite series of queues. Schonmann will consider problems in interacting particle systems and large deviations: metastability for stochastic Ising models, critical behavior of cellular automata, and large deviations for random fields. The principal investigators will conduct research on several problems in probability theory. The primary focus will be on interacting systems of particles. These systems arise in modeling physical and biological systems, and have applications in other areas, such as computer science.