Fluctuations of Functions of Wigner Matrices
  We show that matrix elements of functions of $N\times N$ Wigner matrices fluctuate on a scale of order $N^{-1/2}$ and we identify the limiting fluctuation. Our result holds for any function $f$ of the matrix that has bounded variation and thus considerably relaxes the regularity requirement imposed in [7,11]. 
L\'aszl\'o Erd\H{o}s and Dominik Schr\"oder
math.PR math-ph math.MP