Large deviation theorem for zeros of polynomials and Hermitian random   matrices
  We give abstract versions of the large deviation theorem for the distribution of zeros of polynomials and apply them to the characteristic polynomials of Hermitian random matrices. We obtain new estimates related to the local semi-circular law for the empirical spectral distribution of these matrices when the 4th moments of their entries are controlled. 
Tien-Cuong Dinh
math.CV math.PR