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Mathematical Physics Seminar

Lyapunov exponents for random products of real matrices

Siddhartha Sahi - Rutgers University

Location:  Hill Center Room 705
Date & time: Thursday, 23 February 2023 at 12:00PM - 1:00PM

Abstract: We consider probability measures on GL(n,R) that are invariant under left multiplication by the orthogonal group O(n,R). For any such measure we compare the mean of the logs of the moduli of eigenvalues of the matrices and the Lyapunov exponents of random matrix products independently drawn with respect to the measure. We give a lower bound for the former in terms of the latter.

This result was conjectured by Burns-Pugh-Shub-Wilkinson (2001), and special cases were proved by Dedieu-Shub (2002), Avila-Bochi (2003) and Rivin (2005).

A novel feature of our treatment is the use of the theory of spherical polynomials in the proof of our main result. This is joint work (arXiv:2206.01091) with Diego Armentano, Gautam Chinta, and Michael Shub

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