## Electronic Journal of Probability

### Synchronization for discrete mean-field rotators

#### Abstract

We analyze a non-reversible mean-field jump dynamics for discrete q-valued rotators and show in particular that it exhibits synchronization. The dynamics is the mean-field analogue of the lattice dynamics investigated by the same authors which provides an example of a non-ergodic interacting particle system on the basis of a mechanism suggested by Maes and Shlosman.

Based on the correspondence to an underlying model of continuous rotators via a discretization transformation we show the existence of a locally attractive periodic orbit of rotating measures. We also discuss global attractivity, using a free energy as a Lyapunov function and the linearization of the ODE which describes typical behavior of the empirical distribution vector.

#### Article information

Source
Electron. J. Probab., Volume 19 (2014), paper no. 14, 26 pp.

Dates
Accepted: 20 January 2014
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465065656

Digital Object Identifier
doi:10.1214/EJP.v19-2948

Mathematical Reviews number (MathSciNet)
MR3164767

Zentralblatt MATH identifier
1288.82042

Rights

#### Citation

Jahnel, Benedikt; Külske, Christof. Synchronization for discrete mean-field rotators. Electron. J. Probab. 19 (2014), paper no. 14, 26 pp. doi:10.1214/EJP.v19-2948. https://projecteuclid.org/euclid.ejp/1465065656

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