Lozenge Tilings and the Gaussian Free Field on a Cylinder
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220_2022_4491_ReferencePDF.pdf
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2.62 MB
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Checksum (MD5)
c2ce64233b4f8e52b1bd9e0c2466aed3
Author(s)
Ahn, Andrew
Russkikh, Marianna
Van Peski, Roger
Date Issued
September 19, 2022
Publisher
Springer Berlin Heidelberg
Citation
Ahn, Andrew, Russkikh, Marianna and Van Peski, Roger. 2022. "Lozenge Tilings and the Gaussian Free Field on a Cylinder."
Version
Author's final manuscript
Abstract
Abstract
We use the periodic Schur process, introduced in (Borodin in Duke Math J 140(3):391–468 2007), to study the random height function of lozenge tilings (equivalently, dimers) on an infinite cylinder distributed under two variants of the
$$q^{{{\text {vol}}}}$$
q
vol
measure. Under the first variant, corresponding to random cylindric partitions, the height function converges to a deterministic limit shape and fluctuations around it are given by the Gaussian free field in the conformal structure predicted by the Kenyon-Okounkov conjecture. Under the second variant, corresponding to an unrestricted dimer model on the cylinder, the fluctuations are given by the same Gaussian free field with an additional discrete Gaussian shift component. Fluctuations of the latter type have been previously conjectured for dimer models on planar domains with holes.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00220-022-04491-x
