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PLEASE NOTE SPECIAL TIME

Let $X_{N,n}$ be an iid product of $N$ real Gaussian matrices of size $n \timesÌýn$. In this talk, I will explain some recent joint work with G. PaourisÌý(arXiv:2005.08899) about a non-asymptoticÌýanalysis of the singular values of $X_{N,n}$. I will begin by giving some intuition and motivation for studyingÌýsuch matrix products.ÌýThen, I will explain two new results. The first givesÌýa rate of convergence for theÌýglobal distribution of singular values of $X_{N,n}$ to the so-called Triangle Law in the limit where $N,n$ tend toÌýinfinity. The second is a kind of quantitative version of the multiplicativeÌýergodic theorem, giving estimates at finite but large $N$ on the distanceÌýbetween the joint distribution of all Lyapunov exponents of $X_{N,n}$ andÌýappropriatelyÌýnormalized independent Gaussians in the near-ergodic regime ($N\ggÌýn$).