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

TL;DR

This paper establishes a frequency-independent bound on trigonometric functions of certain Gaussian random fields, simplifying the analysis of singular stochastic PDEs and broadening the applicability of existing models.

Contribution

It introduces a novel frequency-independent bound on Gaussian trigonometric functions, reducing regularity assumptions in key stochastic PDE models.

Findings

Bound applies to singular Gaussian fields in stochastic PDEs

Enables weaker regularity assumptions in KPZ and $\

Abstract

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.