Anderson localization and extreme values in chaotic climate dynamics

TL;DR

This paper investigates the connection between Anderson localization and extreme value statistics in chaotic climate dynamics, proposing a new diagnostic tool based on the GEV shape parameter to distinguish localized from delocalized systems.

Contribution

It introduces a novel approach combining Random Matrix Theory and extremal limit laws to analyze wave localization phenomena in climate models.

Findings

GEV shape parameter $\xi$ effectively differentiates localized and delocalized states.

The approach links wave transport phenomena with extreme value theory.

Provides a physical proof of state transition properties for extreme value processes.

Abstract

This work is a generic advance in the study of delocalized (ergodic) to localized (non-ergodic) wave propagation phenomena in the presence of disorder. There is an urgent need to better understand the physics of extreme value process in the context of contemporary climate change. For earth system climate analysis General Circulation Model simulation sizes are rather small, 10 to 50 ensemble members due to computational burden while large ensembles are intrinsic to the study of Anderson localization. We merge universal transport approaches of Random Matrix Theory (RMT), described by the characteristic polynomial of random matrices, with the geometrical universal extremal types max stable limit law. A generic ensemble based random Hamiltonian approach allows a physical proof of state transition properties for extreme value processes. In this work Anderson localization is examined for the extreme tails of the related probability densities. We show that the Generalized Extreme Value (GEV) shape parameter $\xi$ is a diagnostic tool that accurately distinguishes localized from delocalized systems and this property should hold for all wave based transport phenomena.