CONVERGENCE OF SPACE-DISCRETISED GKPZ VIA REGULARITY STRUCTURES

• 成果类型: Article
• 署名作者: Bruned, Yvain; Nadeem, Usama
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; University of Edinburgh; Heriot Watt University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2029
• 发表日期: 2024
• 页码: 2488-2538
• 关键词: RENORMALIZATION; MODEL

摘要

In this work, we show a convergence result for the discrete formulation of the generalised KPZ equation Bt u = (Au) +g(u)(Vu)2 +k(Vu) +h(u) + f (u)xi t(x), where xi is real -valued, A is the discrete Laplacian, and V is a discrete gradient, without fixing the spatial dimension. Our convergence result is established within the discrete regularity structures introduced by Hairer and Erhard (Ann. Inst. Henri Poincare Probab. Stat. 55 (2019) 2209-2248). We extend with new ideas the convergence result found in (Comm. Pure Appl. Math. 77 (2024) 1065-1125) that deals with a discrete form of the parabolic Anderson model driven by a (rescaled) symmetric simple exclusion process. This is the first time that a discrete generalised KPZ equation is treated and it is a major step toward a general convergence result that will cover a large family of discrete models.