Abstract:We investigate concentration properties of spectral measures of Hermitian random matrices with partially dependent entries. More precisely, let Xn be a Hermitian random matrix of size n × n that can be split into independent blocks of the size at most dn = o(n 2 ). We prove that under some mild conditions on the distribution of the entries of Xn, the empirical spectral measure of Xn concentrates around its mean.The main theorem is a strengthening of a recent result by Kemp and Zimmerman, where the size of bloc… Show more
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