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A Gaussian distribution for refined DT invariants and 3D partitions

Authors
  • Morrison, Andrew
Type
Preprint
Publication Date
Mar 15, 2013
Submission Date
Mar 15, 2013
Identifiers
DOI: 10.1007/s00220-014-2051-8
Source
arXiv
License
Yellow
External links

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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