In this paper we study the typical profiles of a random field Kac
model. We give upper and lower bounds of the space scale where the profiles are
constant. The results hold almost surely with respect to the realizations of
the random field. The analysis is based on a block-spin construction, deviation
techniques for the local empirical order parameters and concentration
inequalities for the realizations of the random magnetic field. For the upper
bound, we exhibit a scale related to the law of the iterated logarithm, where
the random field makes an almost sure fluctuation that obliges the system to
break its rigidity. For the lower bound, we prove that on a smaller scale the
fluctuations are not strong enough to allow this transition.
Publié le : 1999-07-14
Classification:
Large deviations,
Kac potentials,
deviation inequality,
local central limit theorem,
law of the iterated logarithm,
60K35,
82B20,
82B43
@article{1022677454,
author = {Cassandro, Marzio and Orlandi, Enza and Picco, Pierre},
title = {Typical Configurations for One-Dimensional Random Field Kac
Model},
journal = {Ann. Probab.},
volume = {27},
number = {1},
year = {1999},
pages = { 1414-1467},
language = {en},
url = {http://dml.mathdoc.fr/item/1022677454}
}
Cassandro, Marzio; Orlandi, Enza; Picco, Pierre. Typical Configurations for One-Dimensional Random Field Kac
Model. Ann. Probab., Tome 27 (1999) no. 1, pp. 1414-1467. http://gdmltest.u-ga.fr/item/1022677454/