FLUCTUATIONS OF STOCHASTIC PDES WITH LONG-RANGE CORRELATIONS

• 成果类型: Article
• 署名作者: Gerolla, Luca; Hairer, Martin; Li, Xue-Mei
• 署名单位: Imperial College London; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2140
• 发表日期: 2025
• 页码: 1198-1232
• 关键词: heat-equation; kpz equation; anisotropic kpz; dimensions 3; limit; BEHAVIOR; particle; THEOREM

摘要

We study the large-scale dynamics of the solution to a nonlinear stochastic heat equation (SHE) in dimensions d >= 3 with long-range dependence. This equation is driven by multiplicative Gaussian noise, which is white in time and coloured in space with nonintegrable spatial covariance that decays at the rate of |x|-kappa at infinity, where kappa E (2, d). Inspired by recent studies on SHE and KPZ equations driven by noise with compactly supported spatial correlation, we demonstrate that the correlations persist in the largescale limit. The fluctuations of the diffusively scaled solution converge to the solution of a stochastic heat equation with additive noise whose correlation is the Riesz kernel of degree-kappa. Moreover, the fluctuations converge as a distribution-valued process in the optimal H & ouml;lder topologies.