One-dimensional random field Kac's model: weak large deviations principle
| dc.creator | Orlandi, Enza | |
| dc.creator | Picco, Pierre | |
| dc.date | 2006-11-22 | |
| dc.date.accessioned | 2026-07-07T07:33:13Z | |
| dc.date.available | 2026-07-07T07:33:13Z | |
| dc.description | We prove 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 Bernoulli random variables. The results are valid for values of the temperature, $β^{-1}$, and magnitude, $θ$, of the field in the region where the free energy of the corresponding random Curie Weiss model has only two absolute minima $m_β$ and $Tm_β$. We give an explicit representation of the rate functional which is a positive random functional determined by two distinct contributions. One is related to the free energy cost ${\cal F}^*$ to undergo a phase change (the surface tension). The ${\cal F}^*$ is the cost of one single phase change and depends on the temperature and magnitude of the field. The other is a bulk contribution due to the presence of the random magnetic field. We characterize the minimizers of this random functional. We show that they are step functions taking values $m_β$ and $Tm_β$. The points of discontinuity are described by a stationary renewal process related to the $h-$extrema for a bilateral Brownian motion studied by Neveu and Pitman, where $h$ in our context is a suitable constant depending on the temperature and on magnitude of the random field. As an outcome we have a complete characterization of the typical profiles of RFKM (the ground states) which was initiated in [14] and extended in [16]. | |
| dc.identifier | https://arxiv.org/abs/math/0611688 | |
| dc.identifier | http://arxiv.org/abs/math/0611688 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119379 | |
| dc.subject | Probability | |
| dc.subject | Primary 60K35, secondary 82B20,82B43 | |
| dc.title | One-dimensional random field Kac's model: weak large deviations principle | |
| dc.type | text |