Lifshitz asymptotics and localization for random quantum waveguides

We investigate a family of Dirichlet Laplacians on randomly dented or bulged strips in R-2; for this random quantum waveguide model, dense point spectrum with exponentially localized eigenfunctions near its fluctuation boundary at the bottom of the spectrum and Lifshitz asymptotics of the integrated density of states are established. For this purpose, multi-scale analysis in the quite abstract form of [21] is applied, and domain perturbations of the Laplacian are studied.