Modeling of an Asymptotically Central Markov Process on 3D Young Graph

The paper discusses the asymptotics of path probabilities in Markov processes close to a central one on 3D Young graph. We consider a one-parameter family of such processes and compute the parameter value in such a way that the centrality condition is satisfied with the greatest possible accuracy. We defined a normalized dimension of paths in the 3D Young graph. We study the growth and oscillations of these normalized dimensions along greedy and random trajectories of the processes using large computer experiments involving 3D Young diagrams with millions of boxes.