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arXiv · 1606.00862

Stochastic Dynamics of Growing Young Diagrams and Their Limit Shapes

P. L. Krapivsky
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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 $\geq r$. 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.

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BibTeXRIS

P. L. Krapivsky. 2020-11-12. Stochastic Dynamics of Growing Young Diagrams and Their Limit Shapes. https://doi.org/10.1088/1742-5468%2Fabd025

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