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

Percy Deift, Thomas Trogdon

Research output: Contribution to journalArticle

Abstract

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
Volume71
Issue number3
DOIs
StatePublished - Mar 1 2018

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Largest Eigenvalue
Random Matrices
Universality
Eigenvalues and Eigenvectors
Hermitian matrix
Eigenvalues and eigenfunctions
Rigidity
Statistics
Fluctuations

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Universality for the Toda Algorithm to Compute the Largest Eigenvalue of a Random Matrix. / Deift, Percy; Trogdon, Thomas.

In: Communications on Pure and Applied Mathematics, Vol. 71, No. 3, 01.03.2018, p. 505-536.

Research output: Contribution to journalArticle

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