## Electronic Communications in Probability

### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 24 (2019), paper no. 2, 10 pp.

Dates
Accepted: 19 December 2018
First available in Project Euclid: 24 January 2019

https://projecteuclid.org/euclid.ecp/1548299047

Digital Object Identifier
doi:10.1214/18-ECP205

Mathematical Reviews number (MathSciNet)
MR3908647

Zentralblatt MATH identifier
1406.60129

#### Citation

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

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