论文标题
晶格上相互作用粒子系统流体力学极限的一致性稳定性方法
A consistence-stability approach to hydrodynamic limit of interacting particle systems on lattices
论文作者
论文摘要
这是基于2021年12月在研讨会劳伦特·施瓦茨（Laurent Schwartz）进行的演讲。这项工作提出了一种新的简单定量方法，用于证明晶格上一类相互作用的粒子系统的流体动力极限。我们在这里以简化的设置，零范围的过程和带有川崎动力学的Ginzburg-Landau过程，在抛物线缩放和尺寸$ 1 $中介绍此方法。收敛速度是定量和均匀的。证明依赖于瓦斯汀距离中的一致性稳定性方法，并避免了``块估计''的使用。
This is a review based on the presentation done at the seminar Laurent Schwartz in December 2021. It is announcing results in the forthcoming [Menegaki-Mouhot-Marahrens'22]. This work presents a new simple quantitative method for proving the hydrodynamic limit of a class of interacting particle systems on lattices. We present here this method in a simplified setting, for the zero-range process and the Ginzburg-Landau process with Kawasaki dynamics, in the parabolic scaling and in dimension $1$. The rate of convergence is quantitative and uniform in time. The proof relies on a consistence-stability approach in Wasserstein distance, and it avoids the use of the ``block estimates''.
