Extreme value problems in Random Matrix Theory and other disordered systems

Details Extreme value problems in Random Matrix Theory and other disordered systems Extreme value problems in Random Matrix Theory and other disordered systems

2007-02-09

arxiv.org/abs/cond-mat/0702244v1

Physics

Condensed Matter

Statistical Mechanics

to appear in JSTAT, proceedings of `Principles of Dynamics of Nonequilibrium Systems', ISI Cambridge 2006

Scientific paper

10.1088/1742-5468/2007/07/P07019

We review some applications of central limit theorems and extreme values statistics in the context of disordered systems. We discuss several problems, in particular concerning Random Matrix Theory and the generalisation of the Tracy-Widom distribution when the disorder has ``fat tails''. We underline the relevance of power-law tails for Directed Polymers and mean-field Spin Glasses, and we point out various open problems and conjectures on these matters. We find that in many instances the assumption of Gaussian disorder cannot be taken for granted.

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