HYDRODYNAMIC LIMIT FOR A 2D INTERLACED PARTICLE PROCESS

• 成果类型: Article
• 署名作者: Lerouvillois, Vincent; Toninelli, Fabio
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Technische Universitat Wien
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1674
• 发表日期: 2022
• 页码: 167-190
• 关键词: viscosity solutions; continuum-limit; growth-process; fluctuations; speed

摘要

The Markov dynamics of interlaced particle arrays, introduced by A. Borodin and P. L. Ferrari in (Comm. Math. Phys. 325 (2014) 603-684), is a classical example of (2 + 1)-dimensional random growth model belonging to the so-called Anisotropic KPZ universality class. In (Comm. Pure Appl. Math. 72 (2018) 620-666), a hydrodynamic limit-the convergence of the height profile, after space/time rescaling, to the solution of a deterministic Hamilton-Jacobi PDE with nonconvex Hamiltonian-was proven when either the initial profile is convex, or for small times, before the solution develops shocks. In the present work, we give a simpler proof, that works for all times and for all initial profiles for which the limit equation makes sense. In particular, the convexity assumption is dropped. The main new idea is a new viewpoint about finite speed of propagation that allows to bypass the need of a priori control of the interface gradients, or equivalently of inter-particle distances.