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 $\ge r$. In the long time limit, appropriately re-scaled Young diagrams approach a limit shape that we compute for each integer $r\ge 0$. 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.

18 pages, 5 figures

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Cited by in corpus (3)

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