Random strict partitions and random shifted tableaux

• Sho Matsumoto ^[1] ; Piotr Sniady ^[2]
  1. [1] Kagoshima University

     Kagoshima University

     Japón

     
  2. [2] Polish Academy of Sciences

     Polish Academy of Sciences

     Warszawa, Polonia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 1, 2020
• Idioma: inglés
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• Resumen

  • We study asymptotics of random shifted Young diagrams which correspond to a given sequence of reducible projective representations of the symmetric groups. We show limit results (Law of Large Numbers and Central Limit Theorem) for their shapes, provided that the representation character ratios and their cumulants converge to zero at some prescribed speed. Our class of examples includes uniformly random shifted standard tableaux with prescribed shape as well as shifted tableaux generated by some natural combinatorial algorithms (such as shifted Robinson–Schensted–Knuth correspondence) applied to a random input.