We present a probabilistic model of the microscopic scenario of dielectric relaxation. We prove a limit theorem for random sums of a special type that appear in the model. By means of the theorem, we show that the presented approach to relaxation phenomena leads to the well known Havriliak-Negami empirical dielectric response provided the physical quantities in the relaxation scheme have heavy-tailed distributions. The mathematical model, presented here in the context of dielectric relaxation, can be applied in the analysis of dynamical properties of other disordered systems.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am30-3-7,
author = {Agnieszka Jurlewicz},
title = {Stochastic foundations of the universal dielectric response},
journal = {Applicationes Mathematicae},
volume = {30},
year = {2003},
pages = {325-336},
zbl = {1052.60078},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-3-7}
}
Agnieszka Jurlewicz. Stochastic foundations of the universal dielectric response. Applicationes Mathematicae, Tome 30 (2003) pp. 325-336. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-3-7/