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One-dimensional random field Kac's model: weak large deviations principle


 
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1. Title Title of document One-dimensional random field Kac's model: weak large deviations principle
 
2. Creator Author's name, affiliation, country Pierre Picco; CNRS
 
2. Creator Author's name, affiliation, country Enza Orlandi; Universita di Roma TRE
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) phase transition, large deviations random walk, random environment, Kac potential
 
3. Subject Subject classification Primary 60K35, secondary 82B20,82B43
 
4. Description Abstract We present a quenched weak large deviations principle for the Gibbs measures of a Random Field Kac Model (RFKM) in one dimension. The external random magnetic field is given by symmetrically distributed Bernouilli random variables. The results are valid for values of the temperature and magnitude of the field in the region where the free energy of the corresponding random Curie Weiss model has only two absolute minimizers. We give an explicit representation of the large deviation rate function and characterize its minimizers. We show that they are step functions taking two values, the two absolute minimizers of the free energy of the random Curie Weiss model. The points of discontinuity are described by a stationary renewal process related to the $h$-extrema of a bilateral Brownian motion studied by Neveu and Pitman, where $h$ depends on the temperature and magnitude of the random field. Our result is a complete characterization of the typical profiles of RFKM (the ground states) which was initiated in [2] and extended in [4].
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) CNR-CNRS-Project 8.005,INFM-Roma; Prin07: 20078XYHYS.; GDRE 224 GREFI-MEFI, CNRS-INdAM INFM-Roma; Prin07: 20078XYHYS.; GDRE 224 GREFI-MEFI, CNRS-INdAM.
 
7. Date (YYYY-MM-DD) 2009-06-16
 
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/662
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-662
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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