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

Weijun Xu

doi:10.1007/s40304-018-0162-9

Communications in Mathematics and Statistics ›› 2018, Vol. 6 ›› Issue (4) : 509 -532. DOI: 10.1007/s40304-018-0162-9

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

Weijun Xu ¹^,²^,^a

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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.

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

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Weijun Xu. Sharp Convergence of Nonlinear Functionals of a Class of Gaussian Random Fields. Communications in Mathematics and Statistics, 2018, 6(4): 509-532 DOI:10.1007/s40304-018-0162-9