Appears in collection : Combinatorics and Arithmetic for Physics: special days

I plan to discuss three problems of extremal statistics in which unusual (but related to each other) features arise: a) statistics of two-dimensional ”stretched” random walks above a semicircle, b) spectral properties of sparse random matrices, c) statistics of one-dimensional paths in the Poissonian field of traps. I will pay attention to the relationship of these problems with the Anderson localization in 1D, and with some number-theoretic properties of eta-Dedekind function.