Random matrices have simple spectrum

Abstract

Let M n =(ξ ij )1≤i,j≤n be a real symmetric random matrix in which the upper-triangular entries ξ ij , i < j and diagonal entries ξ ii are independent. We show that with probability tending to 1, M n has no repeated eigenvalues. As a corollary, we deduce that the Erdős-Rényi random graph has simple spectrum asymptotically almost surely, answering a question of Babai.

Locations

• COMBINATORICA - View
• arXiv (Cornell University) - View - PDF
• COMBINATORICA - View
• arXiv (Cornell University) - View - PDF
• COMBINATORICA - View
• arXiv (Cornell University) - View - PDF