Distribution functions for largest eigenvalues and their applications

Details Distribution functions for largest eigenvalues and their applications Distribution functions for largest eigenvalues and their applications

2002-10-17

arxiv.org/abs/math-ph/0210034v2

Proceedings of the ICM, Beijing 2002, vol. 1, 587--596

Physics

Mathematical Physics

Scientific paper

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.

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