Distribution functions for largest eigenvalues and their applications

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 Painlevé II function, are described and their occurences surveyed.

References in corpus (1)

• Toeplitz determinants, random growth and determinantal processes

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• A universality property for last-passage percolation paths close to the axis