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2020 Hydrodynamic limit of a $(2+1)$-dimensional crystal growth model in the anisotropic KPZ class
Vincent Lerouvillois
Electron. J. Probab. 25: 1-35 (2020). DOI: 10.1214/20-EJP473


We study a model, introduced initially by Gates and Westcott [11] to describe crystal growth evolution, which belongs to the Anisotropic KPZ universality class [19]. It can be thought of as a $(2+1)$-dimensional generalisation of the well known ($1+1$)-dimensional Polynuclear Growth Model (PNG). We show the full hydrodynamic limit of this process i.e the convergence of the random interface height profile after ballistic space-time scaling to the viscosity solution of a Hamilton-Jacobi PDE: $\partial _{t}u = v(\nabla u)$ with $v$ an explicit non-convex speed function. The convergence holds in the strong almost sure sense.


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Vincent Lerouvillois. "Hydrodynamic limit of a $(2+1)$-dimensional crystal growth model in the anisotropic KPZ class." Electron. J. Probab. 25 1 - 35, 2020.


Received: 14 October 2019; Accepted: 27 May 2020; Published: 2020
First available in Project Euclid: 8 July 2020

MathSciNet: MR4125781
Digital Object Identifier: 10.1214/20-EJP473

Primary: 60J25 , 60K35 , 82C24

Keywords: anisotropic KPZ , Hydrodynamic limit , Interface growth


Vol.25 • 2020
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