Local semicircle law with imprimitive variance matrix Ajanki, Oskari H Erdös, László ; https://orcid.org/0000-0001-5366-9603 Krüger, Torben H ; https://orcid.org/0000-0002-4821-3297 ddc:570 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. Institute of Mathematical Statistics 2014 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/2179 https://research-explorer.ista.ac.at/download/2179/4729 Ajanki OH, Erdös L, Krüger TH. Local semicircle law with imprimitive variance matrix. <i>Electronic Communications in Probability</i>. 2014;19. doi:<a href="https://doi.org/10.1214/ECP.v19-3121">10.1214/ECP.v19-3121</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1214/ECP.v19-3121 info:eu-repo/semantics/altIdentifier/wos/000341869300001 https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess