The Toda lattice and universality for the computation of the eigenvaleues of a random matrix / Percy Deift, Guillaume Dubach, Carlos Tomei, Thomas Trogdon.

Format:

Book

Author/Creator:

Deift, Percy, 1945- Author.

Dubach, Guillaume, author.

Tomei, Carlos, author.

Trogdon, Thomas D., author.

Series:

London Mathematical Society lecture note series ; 500.

London Mathematical Society lecture note series ; 500

Language:

English

Subjects (All):

Lattice theory.

Eigenvalues.

Hamiltonian systems.

Random matrices.

Physical Description:

1 online resource (x, 161 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2026.

Summary:

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on a 2019 course at the Courant Institute to provide a comprehensive introduction to the area, including previously unpublished results.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.

Contents:

Hamiltonian mechanics and integrable systems

The Toda lattice

Toda without Hamiltonian structure

Random matrix ensembles

Universality for the Toda algorithm.

Notes:

Title from publisher's bibliographic system (viewed on 28 Oct 2025).

ISBN:

1-009-66437-9

1-009-66433-6

9781009664332