Local semicircle law with imprimitive variance matrix

Ajanki O, Erdos L, Krueger T (2014)

Publication Type: Journal article

Publication year: 2014


Book Volume: 19

DOI: 10.1214/ECP.v19-3121


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.

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


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

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