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- W2900011310 abstract "Abstract We study a two‐dimensional stochastic interface growth model that is believed to belong to the so‐called anisotropic KPZ (AKPZ) universality class [4,5]. It can be seen either as a two‐dimensional interacting particle process with drift that generalizes the one‐dimensional Hammersley process [1,24], or as an irreversible dynamics of lozenge tilings of the plane [5,29]. Our main result is a hydrodynamic limit: the interface height profile converges, after a hyperbolic scaling of space and time, to the solution of a nonlinear first‐order PDE of Hamilton‐Jacobi type with nonconvex Hamiltonian (nonconvexity of the Hamiltonian is a distinguishing feature of the AKPZ class). We prove the result in two situations: (1) for smooth initial profiles and times smaller than the time T shock when singularities (shocks) appear or (2) for all times, including t > T shock , if the initial profile is convex. In the latter case, the height profile converges to the viscosity solution of the PDE. As an important ingredient, we introduce a Harris‐type graphical construction for the process. © 2018 Wiley Periodicals, Inc." @default.
- W2900011310 created "2018-11-16" @default.
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- W2900011310 date "2018-11-10" @default.
- W2900011310 modified "2023-10-12" @default.
- W2900011310 title "Hydrodynamic Limit and Viscosity Solutions for a Two-Dimensional Growth Process in the Anisotropic KPZ Class" @default.
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- W2900011310 doi "https://doi.org/10.1002/cpa.21796" @default.
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