Skip to main content

Wigner's matrices; more moments estimates

  • 1663 Accesses

Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 1957)

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

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alice Guionnet .

Rights and permissions

Reprints 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