Survival probability approach to the relaxation of a macroscopic system in the defect-diffusion framework

Volume 31 / 2004

Paulina Hetman Applicationes Mathematicae 31 (2004), 423-432 MSC: 60G50, 60G70, 82C44. DOI: 10.4064/am31-4-4


The main objective of this paper is to present a new probabilistic model underlying the universal relaxation laws observed in many fields of science where we associate the survival probability of the system's state with the defect-diffusion framework. Our approach is based on the notion of the continuous-time random walk. To derive the properties of the survival probability of a system we explore the limit theorems concerning either the summation or the extremes: maxima and minima. The forms of the survival probability that result from the scheme under consideration are in agreement with the characteristics of empirical data. Moreover, the proposed approach allows us to indicate their origins.


  • Paulina HetmanInstitute of Mathematics and Computer Science
    Opole University
    Oleska 48
    45-052 Opole, Poland

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