[17] A determinantal point process approach to scaling and local limits of random Young tableaux (with Cédric Boutillier, Valentin Féray and Pierre-Loïc Méliot). To appear in Annals of Probability.

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: 

  •  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;
  • a simple criteria to determine if the limiting surface is continuous in the whole domain;
  •  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.


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