CLT with explicit variance for products of random singular matrices related to Hill’s equation

We prove a central limit theorem (CLT) for the product of class random singular matrices related to Hill’s equation studied by Adams–Bloch–Lagarias. The CLT features an explicit formula variance in terms distribution matrix entries and this allows exact calculation some examples. Our proof relies on novel connection theory [Formula: see text]-dependent sequences which also leads interesting precise nondegeneracy condition.