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The Semicircle Law for Matrices with Independent Diagonals

Matthias Löwe, Olga Friesen,
published 2011-09-15

We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and independent diagonals. Along the diagonals the entries may be correlated. We show that under sufficiently nice moment conditions the empirical eigenvalue distribution converges almost surely weakly to the semicircle law.

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