Stochastic foundations of the universal dielectric response

• Autorzy: Agnieszka Jurlewicz
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60G50: Sums of independent random variables; random walks
• 82C31: Stochastic methods (Fokker-Planck, Langevin, etc.)
• 60F05: Central limit and other weak theorems
• 82C44: Dynamics of disordered systems (random Ising systems, etc.)
• 60E07: Infinitely divisible distributions; stable distributions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2003
• Tom: 30
• Numer: 3
• Strony: 325-336

Daty

wydano

2003

Twórcy

autor

Agnieszka Jurlewicz

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

Identyfikatory

DOI

10.4064/am30-3-7