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 | |
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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