Random matrices have simple spectrum
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- Tao, T. & Vu, V. Combinatorica (2017). doi:10.1007/s00493-016-3363-4
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Let Mn =(ξij)1≤i,j≤n be a real symmetric random matrix in which the upper-triangular entries ξij, i < j and diagonal entries ξii are independent. We show that with probability tending to 1, Mn 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.