论文标题
在尺寸扩散缩放下的非对称零范围过程的平衡扰动$ d \ geq 2 $
Equilibrium Perturbations for Asymmetric Zero Range Process under Diffusive Scaling in Dimensions $d \geq 2$
论文作者
论文摘要
我们考虑尺寸的不对称零范围过程$ d \ geq 2 $。假设初始密度曲线是恒定密度的扰动，该密度具有$ n^{ - α} $，$α\ in（0,1）$的顺序，并且沿着漂移方向是恒定的。在这里，$ n $是缩放参数。我们表明，在对零范围过程的跳跃速率的某些限制下，受扰动的数量宏观遵守扩散缩放下的热方程。
We consider the asymmetric zero range process in dimensions $d \geq 2$. Assume the initial density profile is a perturbation of the constant density, which has order $N^{-α}$, $α\in (0,1)$, and is constant along the drift direction. Here, $N$ is the scaling parameter. We show that under some constraints on the jump rate of the zero range process, the perturbed quantity macroscopically obeys the heat equation under diffusive scaling.
