Anomalous transport and diffusion versus extreme value theory

In the present work we match the biased hierarchical continuous-time random flight (HCTRF) on a regular lattice (based on hierarchical waiting-time distribution) and the extreme event theory (EVT). This approach extends the understanding of the anomalous transport and diffusion (for example, found in some amorphous, vitreous solids as well as in conducting and light-emitting organic polymers). Both independent approaches were developed in terms of random-trap or valley model where the disorder of energy landscape is exponentially distributed while the corresponding mean residence times in traps obey the power-law. This type of disorder characterizes several amorphous (even used commercially) materials which makes it possible to apply the HCTRF formalism. By using the EVT we additionally show that the rare (stochastic) events are indeed responsible for the transport and diffusion in these materials.