Stochastic foundations of the universal dielectric response

Agnieszka Jurlewicz¹

¹ Hugo Steinhaus Center for Stochastic Methods and Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland

Applicationes Mathematicae, Tome 30 (2003) no. 3, pp. 325-336

Résumé

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.

Détail

DOI : 10.4064/am30-3-7

Keywords: present probabilistic model microscopic scenario dielectric relaxation prove limit theorem random sums special type appear model means theorem presented approach relaxation phenomena leads known havriliak negami empirical dielectric response provided physical quantities relaxation scheme have heavy tailed distributions mathematical model presented here context dielectric relaxation applied analysis dynamical properties other disordered systems