Dimer configurations and interlaced particles on the cylinder

  A dimer configuration of a graph is a subset of the edges, such that every vertex is contained in exactly one edge of the subset. We consider dimer configurations of the honeycomb lattice on the cylinder, which are known to be equivalent to configurations of interlaced particles. Assigning a measure to the set of all such configurations, we show that the probability that particles are located in any subset of points on the cylinder can be written as a determinant, i.e. that the process is determinantal. We also examine Markov chains of interlaced particles on the circle, with dynamics equivalent to RSK.