### 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 language | English (US) |
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Pages (from-to) | 505-536 |

Number of pages | 32 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 71 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2018 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Deift, P., & Trogdon, T. (2018). Universality for the Toda Algorithm to Compute the Largest Eigenvalue of a Random Matrix.

*Communications on Pure and Applied Mathematics*,*71*(3), 505-536. https://doi.org/10.1002/cpa.21715