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A Gaussian Distribution for Refined DT Invariants and 3D Partitions

Morrison, Andrew

In: Communications in Mathematical Physics, 2014, vol. 331, no. 3, p. 1029-1039

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    Title
    • A Gaussian Distribution for Refined DT Invariants and 3D Partitions
    Author
    • Morrison, Andrew. ETH Zurich, Zurich, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Communications in Mathematical Physics, 2014, vol. 331, no. 3, p. 1029-1039. Springer Berlin Heidelberg
    Other Version
    Classification
    • Mathematics
    OAI-PMH Identifier
    • oai:doc.rero.ch:326466
    Summary
    We show that the refined Donaldson-Thomas invariants of $${\mathbb{C}^3}$$ C 3 , suitably normalized, have a Gaussian distribution as limit law. Combinatorially, these numbers are given by weighted counts of 3D partitions. Our technique is to use the Hardy-Littlewood circle method to analyze the bivariate asymptotics of a q-deformation of MacMahon's function. The proof is based on that of E.M. Wright, who explored the single variable case.