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:

arXiv eprints
 Pub Date:
 November 2018
 DOI:
 10.48550/arXiv.1811.01035
 arXiv:
 arXiv:1811.01035
 Bibcode:
 2018arXiv181101035C
 Keywords:

 Mathematics  Probability;
 60K35
 EPrint:
 10 pages, 1 figure