Stochastic Dynamics of Growing Young Diagrams and Their Limit Shapes
  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 $\geq r$. In the long time limit, appropriately re-scaled Young diagrams approach a limit shape that we compute for each integer $r\geq 0$. 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. 
P. L. Krapivsky
cond-mat.stat-mech math-ph math.MP math.PR