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The role of disorder in the dynamics of critical fluctuations of mean field models


 
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1. Title Title of document The role of disorder in the dynamics of critical fluctuations of mean field models
 
2. Creator Author's name, affiliation, country Francesca Collet; Universidad Carlos III de Madrid; Spain
 
2. Creator Author's name, affiliation, country Paolo Dai Pra; Universita' di Padova; Italy
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Disordered models, Interacting particle systems, Mean field interaction, Perturbation theory
 
3. Subject Subject classification 60K35; 82C44
 
4. Description Abstract

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).
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2012-03-23
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1896
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1896
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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