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Limit theorems for the tagged particle in exclusion processes on regular trees
Dayue Chen, Peng Chen, Nina Gantert, Dominik Schmid · 2018-11-03 · via math.PR updates on arXiv.org

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.

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