This 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 where only one impurity is contained, 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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Algebra and Number Theory
- Information Systems
- Computational Theory and Mathematics