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

Ohad N. Feldheim; Sasha Sodin

doi:10.1007/s00039-010-0055-x

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 journal › Article › peer-review

105 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 language	English
Pages (from-to)	88-123
Number of pages	36
Journal	Geometric and Functional Analysis
Volume	20
Issue number	1
DOIs	https://doi.org/10.1007/s00039-010-0055-x
State	Published - Jun 2010
Externally published	Yes

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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10.1007/s00039-010-0055-x

Cite this

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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 P{\'e}ch{\'e}.",

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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.",

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KW - Non-backtracking paths

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KW - Universality

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

Abstract

Bibliographical note

Keywords

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