Universality for the Toda Algorithm to Compute the Largest Eigenvalue of a Random Matrix

Percy Deift, Thomas Trogdon

Research output: Contribution to journalArticle


We prove universality for the fluctuations of the halting time for the Toda algorithm to compute the largest eigenvalue of real symmetric and complex Hermitian matrices. The proof relies on recent results on the statistics of the eigenvalues and eigenvectors of random matrices (such as delocalization, rigidity, and edge universality) in a crucial way.

Original languageEnglish (US)
Pages (from-to)505-536
Number of pages32
JournalCommunications on Pure and Applied Mathematics
Issue number3
StatePublished - Mar 2018


ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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