Sharp Convergence of Nonlinear Functionals of a Class of Gaussian Random Fields

Abstract

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.

Keywords

Multi-point correlation function / Trigonometric polynomial / Gaussian random fields

References

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Funding

Engineering and Physical Sciences Research Council(EP/N021568/1)