Stochastic dynamics of growing Young diagrams and their limit shapes

Abstract

We investigate a class of Young diagrams growing via the addition of unit cells and satisfying the constraint that the height difference between adjacent columns ⩾r. In the long time limit, appropriately re-scaled Young diagrams approach a limit shape that we compute for each integer r ⩾ 0. We also determine limit shapes of ‘diffusively’ growing Young diagrams satisfying the same constraint and evolving through the addition and removal of cells that proceed with equal rates.