Mathematical Sciences: Random Fields

该项目的主要研究人员将是博士后， 首席调查员 研究人员将继续他的 研究随机场 无穷维概率 空间提供了研究欧几里得的极好模型 量子场论和平衡统计力学。 的 概率空间提供了具有参数的模型， 对应于温度、动量截止和耦合常数 等等. 各种现象，如相变，对称性 重正化的破坏和后果可以通过 改变这些参数。 除了在非常简单的情况下， 要证明这些预言是很困难的 严格地 研究人员将尝试攻击其中的一些 有趣的问题，通过使用技术，从非均匀 高斯过程与自由马尔可夫场。

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.