Stochastic foundations of the universal dielectric response

Volume 30 / 2003

Agnieszka Jurlewicz Applicationes Mathematicae 30 (2003), 325-336 MSC: 60E07, 60F05, 60G50, 82C31, 82C44. DOI: 10.4064/am30-3-7


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.


  • Agnieszka JurlewiczHugo Steinhaus Center for Stochastic Methods
    Institute of Mathematics
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland

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