### 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 1 2018 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*71*(3), 505-536. https://doi.org/10.1002/cpa.21715

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

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 71, no. 3, pp. 505-536. https://doi.org/10.1002/cpa.21715

}

TY - JOUR

T1 - Universality for the Toda Algorithm to Compute the Largest Eigenvalue of a Random Matrix

AU - Deift, Percy

AU - Trogdon, Thomas

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85040774557&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040774557&partnerID=8YFLogxK

U2 - 10.1002/cpa.21715

DO - 10.1002/cpa.21715

M3 - Article

AN - SCOPUS:85040774557

VL - 71

SP - 505

EP - 536

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 3

ER -