Connection between Dispersive Transport and Statistics of Extreme Events

TL;DR

This paper links dispersive transport in amorphous materials to extreme event statistics, explaining the length-dependent mobility through the distribution of maximum values in samples.

Contribution

It introduces a statistical framework connecting dispersive transport phenomena to extreme value theory, providing analytical expressions for related quantities.

Findings

Mobility scales with length as a power law with exponent related to extreme value statistics.

Derived formulas for maximum values in samples for exponential and power-law distributions.

Provides a theoretical basis for understanding dispersive transport behavior.

Abstract

A length dependence of the effective mobility in the form of a power law, B ~ L^(1-1/alpha) is observed in dispersive transport in amorphous substances, with 0 < \alpha < 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.