Local semicircle law with imprimitive variance matrix

O.H. Ajanki, L. Erdös, T.H. Krüger, Electronic Communications in Probability 19 (2014).

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Journal Article | Published | English
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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.
Publishing Year
Date Published
2014-06-09
Journal Title
Electronic Communications in Probability
Volume
19
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Ajanki OH, Erdös L, Krüger TH. Local semicircle law with imprimitive variance matrix. Electronic Communications in Probability. 2014;19. doi:10.1214/ECP.v19-3121
Ajanki, O. H., Erdös, L., & Krüger, T. H. (2014). Local semicircle law with imprimitive variance matrix. Electronic Communications in Probability, 19. https://doi.org/10.1214/ECP.v19-3121
Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Local Semicircle Law with Imprimitive Variance Matrix.” Electronic Communications in Probability 19 (2014). https://doi.org/10.1214/ECP.v19-3121.
O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local semicircle law with imprimitive variance matrix,” Electronic Communications in Probability, vol. 19, 2014.
Ajanki OH, Erdös L, Krüger TH. 2014. Local semicircle law with imprimitive variance matrix. Electronic Communications in Probability. 19.
Ajanki, Oskari H., et al. “Local Semicircle Law with Imprimitive Variance Matrix.” Electronic Communications in Probability, vol. 19, Institute of Mathematical Statistics, 2014, doi:10.1214/ECP.v19-3121.
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