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HK: Fachverband Physik der Hadronen und Kerne
HK 34: Postersitzung
HK 34.74: Poster
Thursday, March 13, 2008, 14:00–16:00, Poster C3
Deformations of Tracy-Widom distributions — •Mauricio Porto Pato1,2, Oriol Bohigas2, and Josue Xavier de Carvalho2,3 — 1Instituto de Física, Universidade de São Paulo Caixa Postal 66318, 05315-970 São Paulo, S.P., Brazil — 2CNRS, Université Paris-Sud, UMR8626, LPTMS, Orsay Cedex, F-91405, France — 3Max-Planck-Institut für Physik komplexer Systeme Nöthnitzer Straβe 38, D-01187 Dresden, Germany
In the beginning of the 90’s, Tracy and Widom derived the probability distributions (TW) of the largest eigenvalues of the three Gaussian ensembles, the orthogonal, the unitary and the symplectic and applications in several different areas have followed.It is by now accepted that these distributions belong to an universal class of extreme values of correlated sequences. However, deviations from them have already been observed and another important issue is the relation they have with known distribution of extreme values of uncorrelated sequences. We address these two points by considering two different models. In the first, disorder is introduced in the Gaussian ensembles by imposing on them an external source of randomness. It is shown that as result there is a competition between TW and other distributions including the normal one. The second model arises from the fact that the TW formalism based on Fredholm determinants and Painlevé equations contains in itself a transition from TW to the Weilbull distribution of extreme values of independent identically distributed sequences.