论文标题
在随机方向上的零范围过程的流体动力极限
Hydrodynamic limit of the zero range process on a randomly oriented graph
论文作者
论文摘要
我们证明了带有两个车道和随机取向边缘的圆环上完全不对称的零范围过程的流体动力极限。不对称意味着该模型是不可逆的。边缘的随机取向是以一种bentosication构建的，该方式使静置的零范围模型保持通常的产品分布固定。它也被安排在Z方向上没有整体漂移，尽管动态中存在不对称性，但表明扩散缩放。实际上，使用相对熵方法，我们证明淬灭的流体动力极限是具有扩散系数的热方程，具体取决于边缘方向的厄贡特性。 该图上的零范围过程被证明是非梯度的。我们的主要新颖性是引入局部平衡度量，将图的顶点分解为恒定密度的组成部分。这些组件的巧妙选择消除了在流体动力极限过程中通常会出现的非梯度问题。
We prove the hydrodynamic limit of a totally asymmetric zero range process on a torus with two lanes and randomly oriented edges. The asymmetry implies that the model is non-reversible. The random orientation of the edges is constructed in a bistochastic fashion which keeps the usual product distribution stationary for the quenched zero range model. It is also arranged to have no overall drift along the Z direction, which suggests diffusive scaling despite the asymmetry present in the dynamics. Indeed, using the relative entropy method, we prove the quenched hydrodynamic limit to be the heat equation with a diffusion coefficient depending on ergodic properties of the orientation of the edges. The zero range process on this graph turns out to be non-gradient. Our main novelty is the introduction of a local equilibrium measure which decomposes the vertices of the graph into components of constant density. A clever choice of these components eliminates the non-gradient problems that normally arise during the hydrodynamic limit procedure.
