BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Product of random matrices depending on a parameter revisited Goldsheid, Ilya


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 $E$.

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