Abstract
We here restrict ourselves to the case where V (x) = ?x 2/4 and for short denote by \(P_\beta ^N\) the law of the eigenvalues (?i)1?i?N:
with
Selberg (cf. [153, Theorem 4.1.1] or [6]) found the explicit formula for \(Z_\beta ^N\) for any ? ? 0:
The knowledge of \(Z_\beta ^N\) up to the second order is crucial below, reason why we restrict ourselves to quadratic potentials in the next theorem (see Exercise 11.4 for a slight extension).
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© 2009 Springer-Verlag Berlin Heidelberg
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Guionnet, A. (2009). Large Deviations of the Maximum Eigenvalue. In: Large Random Matrices: Lectures on Macroscopic Asymptotics. Lecture Notes in Mathematics(), vol 1957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69897-5_12
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DOI: https://doi.org/10.1007/978-3-540-69897-5_12
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