An asymptotic link between LUE and GUE and its spectral interpretation

Details An asymptotic link between LUE and GUE and its spectral interpretation An asymptotic link between LUE and GUE and its spectral interpretation

2002-04-13

arxiv.org/abs/math/0204175v1

Mathematics

Probability

15 pages, 1 figure

Scientific paper

We use a matrix central-limit theorem which makes the Gaussian Unitary Ensemble appear as a limit of the Laguerre Unitary Ensemble together with an observation due to Johansson in order to derive new representations for the eigenvalues of GUE. For instance, it is possible to recover the celebrated equality in distribution between the maximal eigenvalue of GUE and a last-passage time in some directed brownian percolation. Similar identities for the other eigenvalues of GUE also appear.

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