Mathematical Sciences: Random Fields

本项目的主要研究人员将是首席研究员的博士后。研究人员将继续他在随机场的工作。无限维概率空间为研究欧几里得量子场论和平衡统计力学提供了很好的模型。提供模型的概率空间具有对应于温度、动量截止和耦合常数等参数。通过改变这些参数，可以预测相变、对称破缺和重整化的后果等各种现象。除了在非常简单的情况下，这些预测的证明很难严格地完成。研究人员将尝试通过使用与自由马尔可夫场相关的非齐次高斯过程的技术来解决这些有趣的问题。

The main researcher for this project will be a post-doc to the principal investigator. The researcher will continue his work on the random fields. Infinite dimensional probability spaces provide excellent models in the study of Eucleadian quantum field theory and equilibrium statistical mechanics. The probability spaces providing the models have parameters that correspond to temperature, momentum cutoff and coupling constants etc.. Various phenomena such as phase transition, symmetry breaking and consequences of renormalization can be predicted by varying these perameters. Except in very simple situations, the proofs of these predictions are difficult to accomplish rigorously. The researcher will try to attack some of these intriguing problems via the use of techniques from nonhomogeneous Gaussian processes associated with the free Markov field.