论文标题
边界驱动的零范围过程
The boundary driven zero-range process
论文作者
论文摘要
我们研究有限晶格$ \ {1，\ ldots，n-1 \} $的对称零范围过程的渐近行为，其边界缓慢，在该站点$ 1 $上创建粒子，或在site $ n \！ - \！1 $上nihihihihihihihihihihihihihihied of nip $ n \！ - \！1 $，其比率为$ n^^{ - ch { - ch { - θ$ $ $ qe $ qe $ qe $ qe $ qe $ qe $ qe for geq $ qe $ ge qe ceq for geq。我们介绍了该模型的不变度量，并获得了静静力极限。为了理解该模型在扩散缩放下的空间演化的渐近行为，我们开始分析流体动力学极限，从而利用吸引力为必不可少的成分。我们获得流体动力方程的边界条件取决于$θ$的值。
We study the asymptotic behaviour of the symmetric zero-range process in the finite lattice $\{1,\ldots, N-1\}$ with slow boundary, in which particles are created at site $1$ or annihilated at site $N\!-\!1$ with a rate proportional to $N^{-θ}$, for $θ\geq 1$. We present the invariant measure for this model and obtain the hydrostatic limit. In order to understand the asymptotic behaviour of the spatial-temporal evolution of this model under the diffusive scaling, we start to analyze the hydrodynamic limit, exploiting attractiveness as an essential ingredient. We obtain that the hydrodynamic equation has boundary conditions that depend on the value of $θ$.
