Abstract
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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© 2003 Springer-Verlag Berlin Heidelberg
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Doumerc, Y. (2003). A note on representations of eigenvalues of classical Gaussian matrices. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVII. Lecture Notes in Mathematics, vol 1832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40004-2_15
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DOI: https://doi.org/10.1007/978-3-540-40004-2_15
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20520-3
Online ISBN: 978-3-540-40004-2
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