Confined random motion with Laplace and Linnik statistics

In this paper we reveal that the conjugate property of Bernstein functions connects the tempered subdiffusion with the confinement. The interpretation of anomalous diffusion tending to the confinement is that diffusive motion, accompanied by multiple-trapping events with infinite mean sojourn time, is transformed into pure jumps, restricted in confined environment. This model, just like the tempered one, is generally valid in a wide class of problems of transport in random media that include live cells, relaxation in heterogeneous substances, and jump-diffusion. A relation of our approach to the popular diffusive diffusivity is explained.

Automated summary

In this paper, we demonstrate the connection between tempered subdiffusion and confinement through the conjugate property of Bernstein functions. The transformation of diffusive motion into pure jumps in a confined environment, accompanied by multiple-trapping events with infinite mean sojourn time, explains the tendency of anomalous diffusion towards confinement. This model has broad applicability in problems of transport in random media, including live cells, relaxation in heterogeneous substances, and jump-diffusion. The relation of our approach to diffusive diffusivity is also explained.