Condensed Matter Theory

Christoph Weiss Cumulants of partitions

Author(s): Christoph Weiss, M. Block, M. Holthaus, G. Schmieder

Cumulants of partitions

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Article: J. Phys. A: Math. Gen. 36, 1827-1844 (2003), IoP

Keywords: Cumulants, partitions

PACS: 05.30.Jp, 05.30.Ch, 02.30.Mv

We utilize the formal equivalence between the number-partitioning problem and a harmonically trapped ideal Bose gas within the microcanonical ensemble for characterizing the probability distribution which governs the number of addends occurring in an unrestricted partition of a natural number n. By deriving accurate asymptotic formulae for its coefficients of skewness and excess, it is shown that this distribution remains non-Gaussian even when n is made arbitrarily large. Both skewness and excess vary substantially before settling to their constant-limiting values for n > 1010.

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