2022/11/24 by Dan Betea, Betea, Dan, Anton Nazarov +3
Mathematics · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2211.13728
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.