We present a self-contained proof of a uniform bound on multi-point correlations of trigonometric functions of a class of Gaussian random fields. It corresponds to a special case of the general situation considered in Hairer and Xu (large-scale limit of interface fluctuation models. ArXiv e-prints arXiv:1802.08192, 2018), but with improved estimates. As a consequence, we establish convergence of a class of Gaussian fields composite with more general functions. These bounds and convergences are useful ingredients to establish weak universalities of several singular stochastic PDEs.

中文翻译：

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一类高斯随机场的非线性泛函的尖锐收敛性。

我们提出了一类高斯随机场的三角函数的多点相关的统一界的自包含证明。它对应于Hairer和Xu（接口波动模型的大规模限制。ArXiv电子版arXiv：1802.08192，2018）中考虑的一般情况的特例，但估计值有所改进。结果，我们建立了一类具有更一般功能的高斯场复合体的收敛性。这些界限和收敛是建立几种奇异随机PDE弱通用性的有用成分。