Extreme value problems in Random Matrix Theory and other disordered systems
统计力学
2009-11-13 v1 无序系统与神经网络
摘要
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.
引用
@article{arxiv.cond-mat/0702244,
title = {Extreme value problems in Random Matrix Theory and other disordered systems},
author = {Giulio Biroli and Jean-Philippe Bouchaud and Marc Potters},
journal= {arXiv preprint arXiv:cond-mat/0702244},
year = {2009}
}
备注
to appear in JSTAT, proceedings of `Principles of Dynamics of Nonequilibrium Systems', ISI Cambridge 2006