Séminaire Lotharingien de Combinatoire, 91B.14 (2024), 12 pp.
Jacopo Borga, Cédric Boutillier, Valentin Féray and Pierre-Loïc Méliot
A determinantal Point Process Approach to Scaling and Local Limits of Random Young Tableaux
Abstract.
We obtain scaling and local limit results for large random
multirectangular Young tableaux
via the asymptotic analysis of a determinantal point process due to
Gorin and Rahman (2019).
In particular, we find an explicit description of the limiting surface,
based on solving a complex-valued polynomial equation.
As a consequence, we find a simple criterion to determine if the
limiting surface is continuous in the whole domain,
implying that, for multirectangular tableaux, the limiting surface
is generically discontinuous.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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