论文标题
绘制促进排除和零范围过程的流体动力学
Mapping hydrodynamics for the facilitated exclusion and zero-range processes
论文作者
论文摘要
在对称和不对称情况下，我们得出了两个退化晶格气体的流体动力极限，即\ emph {促进的排除过程}（FEP）和\ emph {促进零范围的过程}（fzrp）。对于这两个过程，对称情况下的流体动力极限采用了扩散的Stefan问题的形式，而不对称情况的特征是双曲线Stefan问题。尽管FZRP很有吸引力，但在两种情况下，我们广泛使用它来得出其流体动力限制的特性，但FEP却不是。为了得出后者的流体动力极限，我们利用了零范围的过程，以及在显微镜和宏观级别上的排除和零范围过程之间的经典映射。由于这两个过程的退化性，不对称情况是一个新的结果，但是我们的工作也比以前在\ cite {Blondel2021stefan}的对称情况下为FEP提出的更简单证明。
We derive the hydrodynamic limit for two degenerate lattice gases, the \emph{facilitated exclusion process} (FEP) and the \emph{facilitated zero-range process} (FZRP), both in the symmetric and the asymmetric case. For both processes, the hydrodynamic limit in the symmetric case takes the form of a diffusive Stefan problem, whereas the asymmetric case is characterized by a hyperbolic Stefan problem. Although the FZRP is attractive, a property that we extensively use to derive its hydrodynamic limits in both cases, the FEP is not. To derive the hydrodynamic limit for the latter, we exploit that of the zero-range process, together with a classical mapping between exclusion and zero-range processes, both at the microscopic and macroscopic level. Due to the degeneracy of both processes, the asymmetric case is a new result, but our work also provides a simpler proof than the one that was previously proposed for the FEP in the symmetric case in \cite{blondel2021stefan}.
