Abstract
We are going to study the limiting spectral measure of fixed dimensional Hermitian block-matrices with large dimensional Wigner blocks. We are going also to identify the limiting spectral measure when the Hermitian block-structure is Circulant. Using the limiting spectral measure of a Hermitian Circulant block-matrix we will show that the spectral measure of a Wigner matrix with $k$-weakly dependent entries need not to be the semicircle law in the limit.
Citation
Tamer Oraby. "The spectral laws of Hermitian block-matrices with large random blocks." Electron. Commun. Probab. 12 465 - 476, 2007. https://doi.org/10.1214/ECP.v12-1335
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