Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 24 (2019), paper no. 2, 10 pp.
Limit theorems for the tagged particle in exclusion processes on regular trees
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.
Electron. Commun. Probab., Volume 24 (2019), paper no. 2, 10 pp.
Received: 2 November 2018
Accepted: 19 December 2018
First available in Project Euclid: 24 January 2019
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Chen, Dayue; Chen, Peng; Gantert, Nina; Schmid, Dominik. Limit theorems for the tagged particle in exclusion processes on regular trees. Electron. Commun. Probab. 24 (2019), paper no. 2, 10 pp. doi:10.1214/18-ECP205. https://projecteuclid.org/euclid.ecp/1548299047