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.

Large scale limit of interface fluctuation models

“…In this case, we will take T = [K] × T , and each point x k,t should be thought of as having a unique type in T . See also [32] for an improvement of Theorem 6.4 in the special case when θ t are equal for all t ∈ T .…”

Generating Functional Multicellular Organoids from Human Placenta Villi

“…UMAP analysis was performed using the RunUMAP function with default parameters. [ 51 ] To validate whether our culture system retained immune components, 3359 cells positive were analyzed for CD45, and use t‐SNE to analyze immune cell subpopulation. Cluster‐specific gene markers were identified using Seurat's FindAllMarkers with cutoffs avg_log2FC > 0.25.…”