Random matrices have simple spectrum.

Let M =( ξ ) be a real symmetric random matrix in which the upper-triangular entries ξ , i < j and diagonal entries ξ are independent. We show that with probability tending to 1, M 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. [ABSTRACT FROM AUTHOR]