The semicircle law for matrices with independent diagonals
  We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and stochastically 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 semi-circle law. 
Olga Friesen and Matthias L\"owe
math.PR math.ST stat.TH