Modelling of measures close to central ones on the three-dimensional Young graph

We describe some computer experiments with 3D Young diagrams for modelling a Markov process whose properties are close to those of the Plancherel growth process in the two-dimensional case. The transition probabilities of this process are defined by formulas that use the lengths of 3D hooks. These formulas were obtained by generalizing well-known formulas for the Plancherel growth process probabilities. Although this 3D Markov process does not generate a central measure, we show that this measure is close to a central one.