A frequency-independent bound on trigonometric polynomials of Gaussians and applications

We prove a frequency-independent bound on trigonometric functions of a class of singular Gaussian random fields, which arise naturally from weak universality problems for singular stochastic PDEs. This enables us to reduce the regularity assumption on the nonlinearity of the microscopic models in KPZ and dynamical $\Phi^4_3$ in [HX19] and [FG19] to that required by PDE structures.