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

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• Exchange Operator Formalism for Integrable Systems of Particles
• Physics and Mathematics of Calogero particles
• Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics
• Equation of State of an Anyon Gas in a Strong Magnetic Field
• Haldane exclusion statistics and second virial coefficient
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• Asymptotic behavior of the length of the longest increasing subsequences of random walks
• Limit shape of minimal difference partitions and fractional statistics
• Large deviations analysis for random combinatorial partitions with counter terms
• Thermodynamics of Statistical Anyons
• Approximately Sampling Elements with Fixed Rank in Graded Posets
• Ergodicity of multiplicative statistics
• A note on limit shapes of minimal difference partitions
• A general asymptotic formula for distinct partitions
• The curious case of operators with spectral density increasing as $\Omega (E)\sim e^{Const.E^2}$
• Extreme statistics and volume fluctuations in a confined one-dimensional gas