Limit theorems for the tagged particle in exclusion processes on regular trees
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2018
- DOI:
- 10.48550/arXiv.1811.01035
- arXiv:
- arXiv:1811.01035
- Bibcode:
- 2018arXiv181101035C
- Keywords:
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- Mathematics - Probability;
- 60K35
- E-Print:
- 10 pages, 1 figure