论文标题
在对称简单排除过程中，当前和标记粒子的中等偏差
Moderate Deviations for the current and Tagged Particle in Symmetric Simple Exclusion Processes
论文作者
论文摘要
我们证明了标记的粒子位置和一维对称简单排除过程中的电流的中等偏差原理。每个位置最多有一个粒子。粒子以$ 1/2 $的价格跳到其两个邻居之一，如果目标站点已经有一个，则会抑制跳跃。我们区分一个称为标记粒子的特定粒子。我们首先建立一个基于GAO和Quastel \ cite {gao2003mporter}证明的基于中等偏差原理的标记粒子位置中等偏差率函数的变异公式。然后，我们构建了变异公式的最小化器，并获得中等偏差率函数的显式表达式。
We prove moderate deviation principles for the tagged particle position and current in one-dimensional symmetric simple exclusion processes. There is at most one particle per site. A particle jumps to one of its two neighbors at rate $1/2$, and the jump is suppressed if there is already one at the target site. We distinguish one particular particle which is called the tagged particle. We first establish a variational formula for the moderate deviation rate functions of the tagged particle positions based on moderate deviation principles from hydrodynamic limit proved by Gao and Quastel \cite{gao2003moderate}. Then we construct a minimizer of the variational formula and obtain explicit expressions for the moderate deviation rate functions.
