2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218092This paper studies the dimer model on the dual graph of the square-octagon lattice, which can be viewed as the domino tilings with impurities in some sense. In particular, under a certain boundary condition, we give an exact formula representing the probability of finding an impurity at a given site in a uniformly random dimer configuration in terms of simple random walks on the square lattice.12pages,12figuresCombinatorics05A15text