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Random matrices have simple spectrum


DOI: 10.1007/s00493-016-3363-4

Cite this article as:
Tao, T. & Vu, V. Combinatorica (2017). doi:10.1007/s00493-016-3363-4


Let Mn =(ξij)1≤i,jn 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.

Mathematics Subject Classification (2000)

05C80 05C50 60C99 

Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsUCLALos AngelesUSA
  2. 2.Department of MathematicsYale UniversityNew HavenUSA

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