二元接触路径过程的流体动力学
Hydrodynamics of the Binary Contact Path Process
摘要：
本文研究了在具有$d\geq 3$的格点$\mathbb{Z}^d$上的\cite{Gri1983}中引入的二元接触路径过程.我们的主要结果给出了该过程的流体动力学极限，这是热方程的解。我们的结果的证明遵循\cite{kipnis+landim99}中引入的策略，给出了SEP模型的流体动力学极限，并对一些细节进行了修改，因为对于二元接触路径过程，所有顶点的状态不是一致有界的。在修改中，利用了在\cite{Lig1985}中引入的线性系的理论。
英文摘要：
In this paper we are concerned with the binary contact path process introduced in \cite{Gri1983} on the lattice $\mathbb{Z}^d$ with $d\geq 3$. Our main result gives a hydrodynamic limit of the process, which is the solution to a heat equation. The proof of our result follows the strategy introduced in \cite{kipnis+landim99} to give hydrodynamic limit of the SEP model with some details modified since the states of all vertices are not uniformly bounded for the binary contact path process. In the modifications, the theory of the linear system introduced in \cite{Lig1985} is utilized.
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