Open Access
2014 Synchronization for discrete mean-field rotators
Benedikt Jahnel, Christof Külske
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Electron. J. Probab. 19: 1-26 (2014). DOI: 10.1214/EJP.v19-2948


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.


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Benedikt Jahnel. Christof Külske. "Synchronization for discrete mean-field rotators." Electron. J. Probab. 19 1 - 26, 2014.


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

zbMATH: 1288.82042
MathSciNet: MR3164767
Digital Object Identifier: 10.1214/EJP.v19-2948

Primary: 60K35
Secondary: 82B26 , 82C22

Keywords: attractive limit cycle , clock model , discretization , interacting particle systems , mean-field sytems , non-equilibrium , rotation dynamics , synchronization , XY model

Vol.19 • 2014
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