Deformations of the Tracy-Widom distribution

Details Deformations of the Tracy-Widom distribution Deformations of the Tracy-Widom distribution

2008-08-18

arxiv.org/abs/0808.2434v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, 1 figure

Scientific paper

10.1103/PhysRevE.79.031117

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.

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