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Cumulants of partitions

Christoph Weiss1, Martin Block1, Martin Holthaus1 and Gerald Schmieder2

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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.


PACS

05.30.Jp Boson systems

05.30.Ch Quantum ensemble theory

37.10.De Atom cooling methods

02.50.Cw Probability theory

MSC

11P83 Partitions; congruences and congruential restrictions

82B10 Quantum equilibrium statistical mechanics (general)

Subjects

Atomic and molecular physics

Quantum gases, liquids and solids

Computational physics

Statistical physics and nonlinear systems

Dates

Issue 7 (21 February 2003)

Received 13 July 2002, in final form 13 November 2002

Published 5 February 2003



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