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

92 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 languageEnglish
Pages (from-to)88-123
Number of pages36
JournalGeometric and Functional Analysis
Volume20
Issue number1
DOIs
StatePublished - Jun 2010

Funding

FundersFunder number
Israel Academy of Sciences and Humanities
Israel Science Foundation

    Keywords

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

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