Limit theorems for the tagged particle in exclusion processes on regular trees

[摘要] We consider exclusion processes on a rooted $d$-regular tree. We start from a Bernoulli product measure conditioned on having a particle at the root, which we call the tagged particle. For $d\geq 3$, we show that the tagged particle has positive linear speed and satisfies a central limit theorem. We give an explicit formula for the speed. As a key step in the proof, we first show that the exclusion process “seen from the tagged particle” has an ergodic invariant measure.

[学科分类] 统计和概率

[关键词] exclusion process;regular tree;tagged particle;ergodicity