For detailed explanations, see http://arxiv.org/abs/1111.7297<br /><br />A dimer tiling is a perfect matching of the cells of a domain of the triangular grid (each cell is grouped with a unique cell to form a rhombi called dimer).<br /><br />A dimer tiling can easily be seen as piles of cubes. A simple local transformation, called flip, which is known to be ergodic on the set of dimer tilings of a domain is removing/adding a cube (that is, turning by 120° a hexagon formed by three rhombi).<br /><br />Now, let us call "error" in a dimer tiling two rhombi identical up to a translation which are adjacent along an edge. Then, draw uniformly at random one of the many possible dimer tilings of a hexagonal domain and run the following discrete time homogeneous Markov chain : draw uniformly at random a vertex and, if it is possible to perform a flip around this vertex, do it if and only if it does not increase the total number of errors in the dimer tiling.<br /><br />Can we bound the hitting time of an error-free dimer tiling?
