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Product of random matrices depending on a parameter revisited

Banff International Research Station for Mathematical Innovation and Discovery

In this talk, I shall consider products of i.i.d. matrices $g_j(t),\ j\ge 1,$ where $t$ is a parameter, $\ t\in T,$ and $T$ is a compact metric space. Matrices $g_(\cdot)$ are continuous functions of $t$. I shall discuss necessary and sufficient conditions under which with probability 1 \[ \frac1n \ln\| g_n(t)\ldots g_1(t)\| \to \lambda(t)\ \ \text{ uniformly in $t\in T$,} \] where $\lambda(t)$ is the corresponding Lyapunov exponent. I shall then explain what happens when $g_j$ are matrices corresponding to the Anderson model and the parameter is the energy $E$.

Mathematics; Operator theory; Dynamical systems and ergodic theory; Mathematical physics

video/mp4

Author affiliation: Queen Mary, University of London

2020-03-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73763

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/