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A determinantal point process approach to scaling and local limits of random Young tableaux
- Publication Year :
- 2023
-
Abstract
- We obtain scaling and local limit results for large random Young tableaux of fixed shape $\lambda^0$ via the asymptotic analysis of a determinantal point process due to Gorin and Rahman (2019). More precisely, we prove: (1) an explicit description of the limiting surface of a uniform random Young tableau of shape $\lambda^0$, based on solving a complex-valued polynomial equation; (2) a simple criteria to determine if the limiting surface is continuous in the whole domain; (3) and a local limit result in the bulk of a random Poissonized Young tableau of shape $\lambda^0$. Our results have several consequences, for instance: they lead to explicit formulas for the limiting surface of $L$-shaped tableaux, generalizing the results of Pittel and Romik (2007) for rectangular shapes; they imply that the limiting surface for $L$-shaped tableaux is discontinuous for almost-every $L$-shape; and they give a new one-parameter family of infinite random Young tableaux, constructed from the so-called random infinite bead process.<br />Comment: New version including referee's corrections, accepted for publication in Annals of Probability
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2307.11885
- Document Type :
- Working Paper