On a class of $H$-selfadjont random matrices with one eigenvalue of nonpositive type

Michal Wojtylak (Jagiellonian University)

Abstract


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.

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Pages: 1-14

Publication Date: October 4, 2012

DOI: 10.1214/ECP.v17-2148

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