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.
Bibliographical noteFunding 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.
- Non-backtracking paths
- Sample covariance
- Tracy Widom