On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder (Q351337)

The Anderson-Bernoulli model with the lattice Laplacian on \(\mathbb{Z}\) and independent random variables in \(\{1,-1\}\) is considered assuring small disorders denoted by the parameter \(\lambda\). It is shown that the Furstenberg measure of the \(\mathrm{SL}_2(\mathbb{R})\)-cocycle has dimension \(\gamma \to 1\) at \(\lambda \to 0\) as well as the integrated density of states is Hölder-regular with the exponent \(s \to 1\) at \(\lambda \to 0\).