Abstract
In this section, we consider the law of N random variables (?1, . . . , ?N) with
for a continuous function V : R ? R such that
and a positive real number ?. Here, ?(?) = ?1?i<j?N(?i ? ?j ).
When V (x) = 4-1?x2, we have seen in Lemma IV that \(P_{4^{ - 1} \beta x^2 ,\beta }^N \) is the law of the eigenvalues of an N ×N GOE (resp. GUE, resp GSE) matrix when ? = 1 (resp. ? = 2, resp. ? = 4). The case ? = 4 corresponds to another matrix ensemble, namely the GSE. In view of these remarks and other applications discussed in Part III, we consider in this section the slightly more general model with a potential V . We emphasize, however, that the distribution (10.1) precludes us from considering random matrices with independent non-Gaussian entries.
Keywords
- Spectral Measure
- Large Deviation Principle
- Concentration Inequality
- Monotone Convergence Theorem
- Bibliographical Note
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 2009 Springer-Verlag Berlin Heidelberg
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Guionnet, A. (2009). Large deviations for the law of the spectral measure of Gaussian Wigner's matrices. 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_11
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DOI: https://doi.org/10.1007/978-3-540-69897-5_11
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Publisher Name: Springer, Berlin, Heidelberg
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