Determinant density and biperiodic alternating links

Abhijit Champanerkar, Ilya Kofman
Let L be any infinite biperiodic alternating link. We show that for any sequence of finite links that Følner converges almost everywhere to L, their determinant densities converge to the Mahler measure of the 2-variable characteristic polynomial of the toroidal dimer model on an associated biperiodic graph.