Distribution functions for largest eigenvalues and their applications
Mathematical Physics
2007-05-23 v2 math.MP
Abstract
It is now believed that the limiting distribution function of the largest eigenvalue in the three classic random matrix models GOE, GUE and GSE describe new universal limit laws for a wide variety of processes arising in mathematical physics and interacting particle systems. These distribution functions, expressed in terms of a certain Painlev\'e II function, are described and their occurences surveyed.
Cite
@article{arxiv.math-ph/0210034,
title = {Distribution functions for largest eigenvalues and their applications},
author = {Craig A. Tracy and Harold Widom},
journal= {arXiv preprint arXiv:math-ph/0210034},
year = {2007}
}