ON A NONLINEAR SPDE DERIVED FROM A HYDRODYNAMIC LIMIT IN A SINAI-TYPE RANDOM ENVIRONMENT

• 成果类型: Article
• 署名作者: Landim, Claudio; Pacheco, Carlos G.; Sethuraman, Sunder; Xue, Jianfei
• 署名单位: Instituto Politecnico Nacional - Mexico; CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional; University of Arizona; University of Missouri System; University of Missouri Columbia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1813
• 发表日期: 2023
• 页码: 200-237
• 关键词: zero-range processes; spectral gap; random conductances; exclusion processes; tagged particle; SCALING LIMITS; random-walks; diffusion; SYSTEM

摘要

With the recent developments on nonlinear SPDEs, where smoothing of rough noises is needed, one is naturally led to study interacting particle systems whose macroscopic evolution is described by these equations and which possess an in-built smoothing. In this article, our main results are to derive regularized versions of the ill-posed one-dimensional SPDE partial derivative(t)rho = 1/2 Delta Phi(rho) - 2 del (W'Phi(rho)),where the spatial white noise W' is replaced by a regularization W'epsilon, as quenched and annealed hydrodynamic limits of zero-range interacting particle systems in epsilon-regularized Sinai-type random environments. Some computations are also made about annealed mean hydrodynamic limits in unregularized Sinai-type random environments with respect to independent particles.