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2012 The role of disorder in the dynamics of critical fluctuations of mean field models
Francesca Collet, Paolo Dai Pra
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Electron. J. Probab. 17: 1-40 (2012). DOI: 10.1214/EJP.v17-1896


The purpose of this paper is to analyze how disorder affects the dynamics of critical fluctuations for two different types of interacting particle system: the Curie-Weiss and Kuramoto model. The models under consideration are a collection of spins and rotators respectively. They both are subject to a mean field interaction and embedded in a site-dependent, i.i.d. random environ- ment. As the number of particles goes to infinity their limiting dynamics become deterministic and exhibit phase transition. The main result con- cerns the fluctuations around this deterministic limit at the critical point in the thermodynamic limit. From a qualitative point of view, it indicates that when disorder is added spin and rotator systems belong to two different classes of universality, which is not the case for the homogeneous models (i.e., without disorder).


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Francesca Collet. Paolo Dai Pra. "The role of disorder in the dynamics of critical fluctuations of mean field models." Electron. J. Probab. 17 1 - 40, 2012.


Accepted: 23 March 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1245.60091
MathSciNet: MR2912503
Digital Object Identifier: 10.1214/EJP.v17-1896

Primary: 60K35
Secondary: 82C44

Keywords: Disordered models , interacting particle systems , mean field interaction , Perturbation theory


Vol.17 • 2012
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