Local semicircle law with imprimitive variance matrix

Ajanki O, Erdos L, Krueger T (2014)

Publication Type: Journal article

Publication year: 2014

Journal

Electronic Communications in Probability Institute of Mathematical Statistics (IMS): OAJ / Institute of Mathematical Statistics

Book Volume: 19

DOI: 10.1214/ECP.v19-3121

Abstract

We extend the proof of the local semicircle law for generalized Wigner matrices given in MR3068390 to the case when the matrix of variances has an eigenvalue -1. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices X*X, where the variances of the entries of X may vary.

Authors with CRIS profile

Torben Krüger

Involved external institutions

IST Austria AT Austria (AT)

How to cite

APA:

Ajanki, O., Erdos, L., & Krueger, T. (2014). Local semicircle law with imprimitive variance matrix. Electronic Communications in Probability, 19. https://doi.org/10.1214/ECP.v19-3121

MLA:

Ajanki, Oskari, Laszlo Erdos, and Torben Krueger. "Local semicircle law with imprimitive variance matrix." Electronic Communications in Probability 19 (2014).

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