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We investigate concentration properties of spectral measures of Hermitianrandom matrices with partially dependent entries. More precisely, let $X_n$ bea Hermitian random matrix of size $n\times n$ that can be split intoindependent blocks of the size at most $d_n=o(n^2)$. We prove that under somemild conditions on the distribution of the entries of $X_n$, the empiricalspectral measure of $X_n$ concentrates around its mean.  The main theorem is a strengthening of a recent result by Kemp and Zimmerman,where the size of blocks grows as $o(\log n)$. As an application, we are ableto upgrade the results of Schenker and Schulz on the convergence in expectationto the semicircle law of a class of random matrices with dependent entries toweak convergence in probability. Other applications include patterned randommatrices, e.g. matrices of Toeplitz, Hankel or circulant type and matrices withheavy tailed entries in the domain of attraction of the Gaussian distribution.

Concentration of the empirical spectral distribution of random matrices with dependent entries