2024/03/10 by Fanhao Kong, Kong, Fanhao, Haiyi Wang +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #Adaptive Control of Nonlinear Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Probability (math.PR) #Sphingolipid Metabolism and Signaling
paper · pdf · doi:10.48550/arxiv.2403.06191
openalex publication_date 2024/03/10 · openalex created_date 2024/03/13 · openalex updated_date 2026/07/28
We consider a class of weakly asymmetric continuous microscopic growth models with polynomial smoothing mechanisms, general nonlinearities and a Poisson type noise. We show that they converge to the KPZ equation after proper rescaling and re-centering, where the coupling constant depends nontrivially on all details of the smoothing and growth mechanisms in the microscopic model. This confirms some of the predictions in [HQ18], and provides a first example of Hairer-Quastel type with both a generic nonlinearity (non-polynomial) and a non-Gaussian noise. The proof builds on the general discretisation framework of regularity structures ([EH19]), and employs the idea of using the spectral gap inequality to control stochastic objects as developed and systematised in [LOTT21,HS24], together with a new observation on the specific structure of the (discrete) Malliavin derivatives in our situation. This structure enables us to reduce the control of mixed Lp spacetime norms (of arbitrarily large p) by certain L2-norms in spacetime.