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On the Toda lattice with random matrix initial data

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HY2W04 - Statistical mechanics, integrability and dispersive hydrodynamics

We consider two regimes for the evolution of the finite Toda lattice with random data in the large-dimensional limit.  First, in the long-time regime, the lattice can be seen as an eigenvalue algorithm and we characterize the distribution of how long the algorithm must run in order to compute the top eigenvalue to a prescribed accuracy.  Second, we consider O(1) times and use a new perturbation theory for orthogonal polynomials to analyze slowly-growing subblocks of the solution. This is joint work with Percy Deift and Xiucai Ding.

This talk is part of the Isaac Newton Institute Seminar Series series.

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