论文标题
2D交织粒子过程的流体动力极限
Hydrodynamic limit for a 2D interlaced particle process
论文作者
论文摘要
A. Borodin和P. Ferrari在Arxiv中引入的交错粒子阵列的Markov动力学：0811.0682，是（2+1） - 维度二维随机生长模型的经典示例，属于所谓的Anisotropic KPZ通用类别。 In Legras-Toninelli (2017) arXiv:1704.06581, a hydrodynamic limit -- the convergence of the height profile, after space/time rescaling, to the solution of a deterministic Hamilton-Jacobi PDE with non-convex Hamiltonian -- was proven when either the initial profile is convex, or for small times, before the solution develops shocks.在目前的工作中，我们提供了一个更简单的证据，可用于所有时间，以及所有初始配置文件，而极限方程式有意义。特别是，凸度假设被删除。主要的新想法是关于“传播有限速度”的一个新观点，该观点允许绕过对接口梯度的A-Priori控制的需求，或者等效于粒子间距离。
The Markov dynamics of interlaced particle arrays, introduced by A. Borodin and P. Ferrari in arXiv:0811.0682, is a classical example of (2+1)-dimensional random growth model belonging to the so-called Anisotropic KPZ universality class. In Legras-Toninelli (2017) arXiv:1704.06581, a hydrodynamic limit -- the convergence of the height profile, after space/time rescaling, to the solution of a deterministic Hamilton-Jacobi PDE with non-convex 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.
