论文标题
通过集群扩展，局部中等和精确的大偏差
Local moderate and precise large deviations via cluster expansions
论文作者
论文摘要
我们考虑一个限制在盒子中的经典粒子系统$λ\ subset \ mathbb {r}^d $，其边界条件通过稳定且常规对的电位相互作用。基于在高温下的群集扩展的有效性 - 低密度状态，我们证明了与颗粒数量平均值相对于大型式吉布斯度量的中等和精确的大偏差。通过这种方式，我们有一种直接的方法来计算指数速率和前因子并获得明确的误差项。还提供了与上述无限体积版本相比的估计。
We consider a system of classical particles confined in a box $Λ\subset\mathbb{R}^d$ with zero boundary conditions interacting via a stable and regular pair potential. Based on the validity of the cluster expansion for the canonical partition function in the high temperature - low density regime we prove moderate and precise large deviations from the mean value of the number of particles with respect to the grand-canonical Gibbs measure. In this way we have a direct method of computing both the exponential rate as well as the pre-factor and obtain explicit error terms. Estimates comparing with the infinite volume versions of the above are also provided.
