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Numerical analysis and random matrix theory

Mathematical Physics & Probability

Speaker: Tom Trogdon, UC Irvine
Related Webpage: https://www.math.uci.edu/~ttrogdon/
Location: 1147 MSB
Start time: Wed, Nov 15 2017, 4:10PM

Numerical analysis and random matrix theory have long been coupled, going (at least) back to the seminal work of Goldstine and von Neumann (1951) on the condition number of random matrices. The works of Trotter (1984) and Silverstein (1985) incorporate numerical techniques to assist in the analysis of random matrices. One can also consider the problem of computing distributions (i.e. Tracy-Widom) from random matrix theory. In this talk, I will discuss different numerical analysis problems: (1) sampling random matrices and (2) using them to analyze the halting time (or runtime) of numerical algorithms. For the latter, I will focus primarily on recent proofs of universality for the (inverse) power method, the QR algorithm and the Toda algorithm. This is joint work with P. Deift, G. Menon, S. Olver and R. Rao.