Integer Partitions and Exclusion Statistics

Abstract

We provide a combinatorial description of exclusion statistics in terms of minimal difference $p$ partitions. We compute the probability distribution of the number of parts in a random minimal $p$ partition. It is shown that the bosonic point $p=0$ is a repulsive fixed point for which the limiting distribution has a Gumbel form. For all positive $p$ the distribution is shown to be Gaussian.

16 pages, 4 .eps figures included

References in corpus (2)

• Physics and Mathematics of Calogero particles
• Level Density of a Bose Gas and Extreme Value Statistics

Cited by in corpus (3)

• A note on limit shapes of minimal difference partitions
• Ergodicity of multiplicative statistics
• Extreme statistics and volume fluctuations in a confined one-dimensional gas