Communications in Mathematical Physics

, Volume 331, Issue 3, pp 1029–1039 | Cite as

A Gaussian Distribution for Refined DT Invariants and 3D Partitions

  • Andrew MorrisonEmail author


We show that the refined Donaldson–Thomas invariants of \({\mathbb{C}^3}\), 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.


Hilbert Scheme Plane Partition Topological Vertex Hard Lefschetz Theorem Thomas Invariant 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.ETH ZurichZurichSwitzerland

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