Deformations of the Tracy-Widom distribution
Statistical Mechanics
2009-11-13 v1 Disordered Systems and Neural Networks
Abstract
In random matrix theory (RMT), the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists in removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristc of extreme values of an uncorrelated sequence, is obtained.
Cite
@article{arxiv.0808.2434,
title = {Deformations of the Tracy-Widom distribution},
author = {O. Bohigas and J. X. de Carvalho and M. P. Pato},
journal= {arXiv preprint arXiv:0808.2434},
year = {2009}
}
Comments
9 pages, 1 figure