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The limiting distribution of the trace of a random plane partition

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Abstract

We study the asymptotic behaviour of the trace (the sum of the diagonal parts) τ n = τ n (ω) of a plane partition ω of the positive integer n, assuming that ω is chosen uniformly at random from the set of all such partitions. We prove that (τ n − c 0 n 2/3)/c 1 n 1/3 log1/2 n converges weakly, as n → ∞, to the standard normal distribution, where c 0 = ζ(2)/ [2ζ(3)]2/3, c 1 = √(1/3/) [2ζ(3)]1/3 and ζ(s) = Σ ∞ j=1 j −s.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, James Bouchier Blvd. 5, Sofia, 1164, Bulgaria

    E. P. Kamenov

  2. American University in Bulgaria, 2700, Blagoevgrad, Bulgaria

    L. R. Mutafchiev

  3. Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences, Acad. G. Bonche str., bl. 8, 1113, Sofia, Bulgaria

    E. P. Kamenov & L. R. Mutafchiev

Authors
  1. E. P. Kamenov
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  2. L. R. Mutafchiev
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Correspondence to E. P. Kamenov.

Additional information

The author was partially supported by the *MRTN-CT-2004-511953* project grant carried out by the Alfréd Rényi Institute of Mathematics in the framework of the European Community’s Program: “Structuring the European Research Area”.

Partial support given by the National Science Fund of the Bulgarian Ministry of Education and Science, grant No. VU-MI-105/2005.

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Kamenov, E.P., Mutafchiev, L.R. The limiting distribution of the trace of a random plane partition. Acta Math Hung 117, 293–314 (2007). https://doi.org/10.1007/s10474-007-6102-x

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  • DOI: https://doi.org/10.1007/s10474-007-6102-x

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