We consider a driven tagged particle in a symmetric exclusion process on Z with a removal rule. In this process, untagged particles are removed once they jump to the left of the tagged particle. We investigate the behavior of the displacement of the tagged particle and prove limit theorems of it: an (annealed) law of large numbers, a central limit theorem, and a large deviation principle. We also characterize a class of ergodic measures for the environment process. Our approach is based on analyzing two auxiliary processes with associated martingales and a regenerative structure.

中文翻译：

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带去除的对称排除过程中的驱动标记粒子

我们在 Z 上的对称排除过程中考虑一个驱动的标记粒子，并带有去除规则。在这个过程中，未标记的粒子一旦跳到标记粒子的左侧就会被移除。我们研究了标记粒子的位移行为并证明了它的极限定理：（退火的）大数定律、中心极限定理和大偏差原理。我们还描述了环境过程的一类遍历测度。我们的方法基于分析具有相关鞅和再生结构的两个辅助过程。