论文标题
通过Boltzmann-Gibbs原理的某些非平稳相互作用粒子系统的波动
Fluctuations for some non-stationary interacting particle systems via Boltzmann-Gibbs Principle
论文作者
论文摘要
Spohn在[Spohn '91]和Jensen-Yau的第7章中的Spohn的猜想II.3.6，要求[Jensen-yau '99]中的猜想要求大规模随机相互作用粒子系统中流体动力限制的通用波动的一般推导。但是，根据[Goncalves-Landim-Milanes '17]，过去几十年来仅目睹了最小的进步。在本文中，我们开发了一种通用方法，用于为普通的不可融合和非平稳相互作用的粒子系统提供所谓的玻尔兹曼 - 吉布斯原理，从而对Spohn和Jensen-Yau做出响应。最重要的是，我们的方法主要取决于模型的局部和动力学，因此更一般/通用的特征。这与以前的作品形成鲜明对比，后者依赖于全球和非宇宙假设，对模型的不变措施或初始度量。作为该方法的具体应用，我们将KPZ方程作为具有环境依赖性不对称性的非平稳性和非综合排除过程的高度功能的大规模限制。这为非平稳和不可融合的“速度更改”模型的大问题问题1.6建立了第一个结果，这些模型也超出了KPZ（de Masi-Presutti-Spohn-Wick '86，Funaki '86，Funaki '18，Funaki-Handa-Handa-handa-harda-uchiyama '91，Komoriya '98]。
Conjecture II.3.6 of Spohn in [Spohn '91] and Lecture 7 of Jensen-Yau in [Jensen-Yau '99] ask for a general derivation of universal fluctuations of hydrodynamic limits in large-scale stochastic interacting particle systems. However, the past few decades have witnessed only minimal progress according to [Goncalves-Landim-Milanes '17]. In this paper, we develop a general method for deriving the so-called Boltzmann-Gibbs principle for a general family of non-integrable and non-stationary interacting particle systems, thereby responding to Spohn and Jensen-Yau. Most importantly, our method depends mostly on local and dynamical, and thus more general/universal, features of the model. This contrasts with previous works, which rely on global and non-universal assumptions on invariant measures or initial measures of the model. As a concrete application of the method, we derive the KPZ equation as a large-scale limit of the height functions for a family of non-stationary and non-integrable exclusion processes with an environment-dependent asymmetry. This establishes a first result to Big Picture Question 1.6 in [AimPLKPZ] for non-stationary and non-integrable "speed-change" models that have also been of interest beyond KPZ [De Masi-Presutti-Spohn-Wick '86, Funaki '18, Funaki-Handa-Uchiyama '91, Komoriya '98].
