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arXiv · 2211.13728

Limit shapes for skew Howe duality

Dan Betea·Anton Nazarov·Travis Scrimshaw
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Abstract

We study large random partitions boxed into a rectangle and coming from skew Howe duality, or alternatively from dual Schur measures. As the sides of the rectangle go to infinity, we obtain: 1) limit shape results for the profiles generalizing the Vershik--Kerov--Logan--Shepp curve; and 2) universal edge asymptotic results for the first parts in the form of the Tracy--Widom distribution, as well as less-universal critical regime results introduced by Gravner, Tracy and Widom. We do this for a large class of Schur parameters going beyond the Plancherel or principal specializations previously studied in the literature, parametrized by two real valued functions $f$ and $g$. Connections to a Bernoulli model of (last passage) percolation are explored.

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Dan Betea, Anton Nazarov, Travis Scrimshaw. 2022-11-24. Limit shapes for skew Howe duality. https://arxiv.org/abs/2211.13728

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