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

Abstract

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.

12 pages, 4 figures (minor typo corrected)

References in corpus (2)

• Level Density of a Bose Gas and Extreme Value Statistics
• Integer Partitions and Exclusion Statistics

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