Abstract
In this chapter, we elaborate upon the previous computation of moments in two directions. First we give a better estimate of the error to the previous limit and prove a central limit theorem. Second, we consider the case where moments are taken at powers that blow up with the dimension of the matrices; we basically show that if this power is small compared to the square root of the dimension, the first-order contribution is still given, in the moment expansion, by graphs that are trees.
Keywords
- Central Limit Theorem
- Large Eigenvalue
- Classical Ensemble
- Moment Estimate
- 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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Guionnet, A. (2009). Wigner's matrices; more moments estimates. 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_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-69897-5_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69896-8
Online ISBN: 978-3-540-69897-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
