Translation invariant Gibbs measures on tilings by Nx1 rectangles

Martin Tassy (Brown University)

Abstract :

For the classic case of 2x1 dominos the set of ergodic Gibbs measures on tilings is well understood and can be characterized by 2 parameters known as the horizontal and vertical slope of the measure. We will show how this result can be extended in a surprising way for Nx1 rectangle tilings through the Conway tiling group. And we will explain why the approach used to obtain our results should be relevant for a large class of non-integrable tilings.