论文标题
在对称简单排除过程中的平衡相关性的大偏差大偏差
Large deviations for out of equilibrium correlations in the symmetric simple exclusion process
论文作者
论文摘要
对于有限的马尔可夫链，唐斯克 - 瓦拉丹理论完全描述了时间平均经验度量的巨大偏差。我们对大尺寸非平衡系统的Donsker-Varadhan理论的扩展感兴趣：与不同密度下的储层相连的一维对称简单排除过程。 Donsker-varadhan功能根据可观察到的感兴趣的具体编码各种量表。在本文中，我们专注于时间平均两个点相关性，并研究与稳态行为的巨大偏差。为了控制平衡的两个点相关性，关键输入是构造与不变度度量的简单近似值。通过在Jara和Menezes Arxiv的工作中建立的相对熵边界估计的时间和空间中，这种近似值是定量的：1810.09526。
For finite size Markov chains, the Donsker-Varadhan theory fully describes the large deviations of the time averaged empirical measure. We are interested in the extension of the Donsker-Varadhan theory for a large size non-equilibrium system: the one-dimensional symmetric simple exclusion process connected with reservoirs at different densities. The Donsker-Varadhan functional encodes a variety of scales depending on the observable of interest. In this paper, we focus on the time-averaged two point correlations and investigate the large deviations from the steady state behaviour. To control two point correlations out of equilibrium, the key input is the construction of a simple approximation to the invariant measure. This approximation is quantitative in time and space as estimated through relative entropy bounds building on the work of Jara and Menezes arXiv:1810.09526.
