论文标题
来自远程排除过程的Kardar-Parisi-Zhang方程
Kardar-Parisi-Zhang Equation from Long-Range Exclusion Processes
论文作者
论文摘要
我们在这里证明，在适当的缩放和重新归一化的情况下，与非简单排除过程相关的高度函数与任意跳高长度收敛到Kardar-Parisi-Zhang SPDE的解决方案。这扩展了Dembo-Tsai'16的工作，以进行任意跳高长度，而Goncalves-Jara '17对于非平稳制度。 Thus we answer a ``Big Picture Question" from the AIM workshop on KPZ and also expand on the almost empty set of non-integrable and non-stationary particle systems for which weak KPZ universality is proven. We use an approximate microscopic Cole-Hopf transform as in Dembo-Tsai'16 but we develop tools to analyze local statistics of the particle system via local equilibrium and work of Goncalves-Jara '17. Local平衡是通过GUO-PAPANICOLAOU-VARADHAN '88中的一个块步骤完成的，用于路径空间/动态统计。
We prove here that the height function associated to non-simple exclusion processes with arbitrary jump-length converges to the solution of the Kardar-Parisi-Zhang SPDE under suitable scaling and renormalization. This extends the work of Dembo-Tsai'16 for arbitrary jump-length and Goncalves-Jara '17 for the non-stationary regime. Thus we answer a ``Big Picture Question" from the AIM workshop on KPZ and also expand on the almost empty set of non-integrable and non-stationary particle systems for which weak KPZ universality is proven. We use an approximate microscopic Cole-Hopf transform as in Dembo-Tsai'16 but we develop tools to analyze local statistics of the particle system via local equilibrium and work of Goncalves-Jara '17. Local equilibrium is done via the one-block step in Guo-Papanicolaou-Varadhan '88 for path-space/dynamic statistics.
