The Toda Lattice and Universality for the Computation of the Eigenvalues of a Random Matrix

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ID: 288060
2025
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Abstract
Written by leaders in the field, this text showcases some of the remarkable properties of the finite Toda lattice and applies this theory to establish universality for the associated Toda eigenvalue algorithm for random Hermitian matrices. The authors expand on a 2019 course at the Courant Institute to provide a comprehensive introduction to the area, including previously unpublished results. They begin with a brief overview of Hamiltonian mechanics and symplectic manifolds, then derive the action-angle variables for the Toda lattice on symmetric matrices. This text is one of the first to feature a new perspective on the Toda lattice that does not use the Hamiltonian structure to analyze its dynamics. Finally, portions of the above theory are combined with random matrix theory to establish universality for the runtime of the associated Toda algorithm for eigenvalue computation.
Reference Key
persistent_1761420318_68fd241ebfa01 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Thomas Trogdon
Journal ADVANCES IN ARCHAEOLOGICAL PRACTICE
Year 2025
DOI
10.1017/9781009664332
URL
https://www.cambridge.org/core/books/toda-lattice-and-universality-for-the-computation-of-the-eigenvalues-of-a-random-matrix/CCD22441001F2CAB251F523308ED01AC
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