Dynamics on interlaced particles

I shall show several models where several interacting particles evolve in time. One arises from the study of tilings by dominoes of a shape in the plane called the Aztec diamond. One is constructed by several Brownian motions reflecting of each other. One comes from a random matrix whose elements evolve in time. For the first two, transition probabilities, respectively densities, can be written down on a nice determinantal form. The last two are determinantal processes along space-like paths which means that certain probabilities there too can be computed by evaluating determinants.