Mathematical Sciences: Stochastic Spatial Models

本研究的领域是相互作用粒子系统，这是相互作用组分的大系统的随机模型。这些系统模拟了诸如物种竞争、流行病、遗传性状传播和催化化学反应等现象。研究者计划研究某些特定种类的相互作用粒子系统的时间极限行为。要研究的具体模型包括选民模型、催化剂模型和相互作用扩散模型。概率论的研究是在相互作用粒子系统的领域。这些是由相互作用的组件组成的大型系统的随机模型。这些系统模拟的现象包括物种竞争、流行病、遗传性状的传播和催化化学反应。

This research is in the area of interacting particle systems, which are stochastic models for large systems of interacting components. These systems model such phenomena as competition of species, epidemics, spread of genetic traits, and catalytic chemical reactions. The investigator plans to study the temporal limit behavior of some particular classes of interacting particle systems. Specific models to be studied include the voter model, a catalyst model, and an interacting diffusion model. This research in probability theory is in the area of interacting particle systems. These are stochastic models for large systems of interacting components. Among the phenomena these systems model are competition of species, epidemics, spread of genetic traits, and catalytic chemical reactions.