solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看200次
Hydrodynamic limit and viscosity solutions for a 2D growth process in the anisotropic KPZ class. (arXiv:1704.06581v1 [math.PR])
来源于:arXiv
We study a $(2+1)$-dimensional stochastic interface growth model, that is
believed to belong to the so-called Anisotropic KPZ (AKPZ) universality class
[Borodin and Ferrari, 2014]. It can be seen either as a two-dimensional
interacting particle process with drift, that generalizes the one-dimensional
Hammersley process [Aldous and Diaconis 1995, Seppalainen 1996], or as an
irreversible dynamics of lozenge tilings of the plane [Borodin and Ferrari
2014, Toninelli 2015]. 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 non-linear first order PDE of Hamilton-Jacobi type with
non-convex Hamiltonian (non-convexity of the Hamiltonian is a distinguishing
feature of the AKPZ class). We prove the result in two situations: (i) for
smooth initial profiles and times smaller than the time $T_{shock}$ when
singularities (shocks) appear or (ii) for all times, including $t>T_{shock}$,
if the initial p 查看全文>>