Electronic Communications in Probability

Limit theorems for the tagged particle in exclusion processes on regular trees

Dayue Chen, Peng Chen, Nina Gantert, and Dominik Schmid

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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
Received: 2 November 2018
Accepted: 19 December 2018
First available in Project Euclid: 24 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1548299047

Digital Object Identifier
doi:10.1214/18-ECP205

Mathematical Reviews number (MathSciNet)
MR3908647

Zentralblatt MATH identifier
1406.60129

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
exclusion process regular tree tagged particle ergodicity

Rights
Creative Commons Attribution 4.0 International License.

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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