Connection between dispersive transport and statistics of extreme events

A length dependence of the effective mobility in the form of a power law, B L1−1/α, is observed in dispersive transport in amorphous substances, with 0<α<1. We deduce this behavior as a simple consequence of the statistical theory of extreme events. We derive various quantities related to the largest value in samples of n trials, for the exponential and power-law probability densities of the individual events.