CONVERGENCES OF THE RESCALED WHITTAKER STOCHASTIC DIFFERENTIAL EQUATIONS AND INDEPENDENT SUMS

• 成果类型: Article
• 署名作者: Chen, Yu-Ting
• 署名单位: University of Victoria
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1753
• 发表日期: 2022
• 页码: 2914-2966
• 关键词: (2+1)d growth; limit; statistics

摘要

We study some SDEs derived from the q -> 1 limit of a 2D surface growth model called the q-Whittaker process. The fluctuations are proven to exhibit Gaussian characteristics that come down from infinity: After rescaling and re-centering, convergences to the time-inverted stationary additive stochastic heat equation (SHE) hold. The point of view in this paper is a novel probabilistic representation of the SDEs by independent sums. By this connection, the normal and Poisson approximations, both in diverging integrated forms, explain the convergence of the re-centered covariance functions. The proof of the process-level convergence identifies additional divergent terms in the dynamics and considers nontrivial cancellations.