Local geometry of the rough-smooth interface in the two-periodic Aztec diamond

Random tilings of the two-periodic Aztec diamond contain three macroscopic regions: frozen, where are deterministic; rough, correlations between dominoes decay polynomially; smooth, exponentially. In a previous paper, authors found that certain averaging height function differences at rough-smooth interface converged to extended Airy kernel point process. this we augment local geometrical picture by introducing well-defined lattice paths which closely related level lines function. We show, after suitable centering and rescaling, process from these converge provided natural parameter associated is small enough.