A Gaussian Distribution for Refined DT Invariants and 3D Partitions
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Date
2014-11
Publication Type
Journal Article
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yes
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Abstract
We show that the refined Donaldson–Thomas invariants of C3, 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.
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published
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Journal / series
Volume
331 (3)
Pages / Article No.
1029 - 1039
Publisher
Springer
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Software
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Subject
Hilbert Scheme; Plane Partition; Topological Vertex; Hard Lefschetz Theorem; Thomas Invariant
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Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.