Séminaire Lotharingien de Combinatoire, 89B.35 (2023), 12 pp.
Dan Betea, Anton Nazarov and Travis Scrimshaw
Limit Shapes for Skew Howe Duality
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.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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