A universality result for the smallest eigenvalues of certain sample covariance matrices

Ohad N. Feldheim, Sasha Sodin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

93 Scopus citations

Abstract

After proper rescaling and under some technical assumptions, the smallest eigenvalue of a sample covariance matrix with aspect ratio bounded away from 1 converges to the Tracy-Widom distribution. This complements the results on the largest eigenvalue, due to Soshnikov and Péché.

Original languageAmerican English
Pages (from-to)88-123
Number of pages36
JournalGeometric and Functional Analysis
Volume20
Issue number1
DOIs
StatePublished - Jun 2010
Externally publishedYes

Bibliographical note

Funding Information:
Keywords and phrases: Universality, sample covariance, Tracy Widom, non-backtracking paths 2010 Mathematics Subject Classification: 60B260B200 The second author is supported in part by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities and by the ISF.

Keywords

  • Non-backtracking paths
  • Sample covariance
  • Tracy Widom
  • Universality

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