Universality for the Toda algorithm to compute the largest eigenvalue of\n a random matrix

2016/04/25 by Percy Deift, Deift, Percy, Thomas Trogdon +1 · 1 citation
Mathematics · #15B52 #65L15 #70H06 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1604.07384

openalex publication_date 2016/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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