Integer partitions and exclusion statistics: Limit shapes and the largest part of Young diagrams

Alain Comtet 1, 2, Satya N. Majumdar 1, Stephane Ouvry 1, Sanjib Sabhapandit 1

Journal of statistical mechanics-theory and experiment (2007) P10001

We compute the limit shapes of the Young diagrams of the minimal difference $p$ partitions and provide a simple physical interpretation for the limit shapes. We also calculate the asymptotic distribution of the largest part of the Young diagram and show that the scaled distribution has a Gumbel form for all $p$. This Gumbel statistics for the largest part remains unchanged even for general partitions of the form $E=\sum_i n_i i^{1/\nu}$ with $\nu>0$ where $n_i$ is the number of times the part $i$ appears.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2. Unite mixte de service de l'institut Henri Poincaré (UMSIHP),
    CNRS : UMS839 – Université Paris VI - Pierre et Marie Curie