TY - JOUR
AB - We consider symmetric random matrices , whose upper triangular entries are independent random variables with zero mean and unit variance. Under the assumption , j, k = 1, 2, ..., n, it is shown that the fluctuations of the Stieltjes transform m(n)(z), of the empirical spectral distribution function of the matrix about the Stieltjes transform of Wigner's semicircle law are of order (n). An application of the result obtained to the convergence rate in probability of the empirical spectral distribution function of to Wigner's semicircle law in the uniform metric is discussed.
AU - GĂ¶tze, Friedrich
AU - Naumov, A. A.
AU - Tikhomirov, A. N.
ID - 2936036
IS - 1
JF - DOKLADY MATHEMATICS
SN - 1064-5624
TI - On Optimal Bounds in the Local Semicircle Law under Four Moment Condition
VL - 99
ER -