"Several works by Tom Wolff related to Anderson-Bernoulli models" Theorem: Let $\mu$ be a probability measure on $PSL(2,\R)$ and assume that supp$\mu$ is not contained in a left coset of an elementary subgroup. Let $\rho$ be a unitary representation such that for some $\e$, the direct integral decomposition of $\rho$ does not contain the trivial representation nor the representations ${\cal C}^u, u>1-\e$. Define $\rho(\mu)=\int\rho(g)d\mu(g)$. Then $\|\rho(\mu)\|<1$. This theorem was first written as an appendix to {\it Some harmonic analysis questions suggested by Anderson-Bernoulli models} by C. Shubin, R. Vakilian, and T.Wolff. This theorem can be generalized to noncompact semi-simple groups. Such groups are connected with products of random matrices; e.g. the Anderson model on the strip with a single site distribution. The main result asserts that if $\mu$ is a probability measure on $G$ contained in $ GL(n,R)$ for which the Zariski closure of the supp$\mu$ is big, then for suitable unitary representations of $\rho$ of $G$, $\hat \mu (\rho)$ has norm less than 1. The key point here being that supp$\mu$ is allowed to be small. We will mention various corollaries and applications of this theorem to the Anderson-Bernoulli models on the strip such as a quantitative bound of the largest Lyapunov exponent for the measure $\nu$ is $> C^{-1}\lambda ^2/n$ where $n$ is the width of the strip, $\lambda$ is the disorder parameter, $C$ a nonzero constant. Also we obtain a refinement of Le Page's theorem on the Holder continuity of the density of states for the Bernoulli model when $n=1$. All three papers will appear in the Journal d'Analyse Mathematique Thomas Wolff Memorial Issue. Many thanks to Editor Larry Zalcman.