一种无树的方法用于三维杨-米尔斯朗之万动态。解析估计与正则结构模型的存在
A tree-free approach to 3D Yang-Mills Langevin dynamic. Analytic estimates and the existence of a model for a regularity structure
AI总结：
本文提出一种无树方法，用于构建三维杨-米尔斯朗之万动态的正则结构模型，并获得全局随机性和点wise加权伯索夫型估计。
摘要：
使用F.Otto等人提出的多索引方法来构建正则结构及其模型，与三维欧几里得杨-米尔斯功能的随机朗之万方程相关联。对于该模型，我们还获得了几乎必然成立的全局随机性和全局点wise加权伯索夫型估计。该模型定义为光滑模型序列的极限，这些模型通过使用平滑噪声引入。当去除平滑时，序列在某种由随机估计定义的拓扑中收敛。为了获得这些结果，我们发展了用于向量值白噪声系统的多索引方法。该项目受构造三维欧几里得杨-米尔斯测度问题的启发，并受作者在相关问题上的先前研究成果的影响，即在闵可夫斯基空间上杨-米尔斯场的规范量子化问题。
英文摘要：
Using the multi-index approach to regularity structures due to F. Otto et al., we construct a regularity structure and a model for it associated to the stochastic Langevin equation for the 3D Euclidean Yang-Mills functional. For the model we also obtain global stochastic and global pointwise weighted Besov type estimates which hold almost surely. The model is defined as a limit of a sequence of smooth models introduced with the help of a mollified noise. When the mollification is removed the sequence converges in a certain topology defined with the help of the stochastic estimates. To obtain these results we develop the multi-index approach for systems of equations with vector-valued white noises. This project is motivated by the problem for constructing 3D Euclidean Yang-Mills measure and by the earlier results of the author on the related problem of canonical quantization of the Yang-Mills field on the Minkowski space.
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