On a class of H-selfadjont random matrices with one eigenvalue of   nonpositive type
  Large H-selfadjoint random matrices are considered. The matrix $H$ is assumed to have one negative eigenvalue, hence the matrix in question has precisely one eigenvalue of nonpositive type. It is showed that this eigenvalue converges in probability to a deterministic limit. The weak limit of distribution of the real eigenvalues is investigated as well. 
Michal Wojtylak
math.FA math.PR