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 the previous works of Hairer-Xu and Furlan-Gubinelli to heuristically optimal thresholds required by PDE structures. This talk is based on the joint work with Fanhao Kong(PKU).
Wenhao Zhao is an undergraduate student at School of Mathematical Sciences, Peking University. He will graduate in July, 2023, and then pursue his PhD at EPFL, advised by Martin Hairer.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai