Abstract
The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions and at sufficiently high temperature, we show that the scaling limit of the infinite-volume gradient Gibbs state with zero mean is a multiple of the Gaussian free field.
This article is the second in a series on the Discrete Gaussian model, extending the methods of the first paper by the analysis of general external fields (rather than macroscopic test functions on the torus). As a byproduct, we also obtain a scaling limit for mesoscopic test functions on the torus.
Funding Statement
R.B. was supported by the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 851682 SPINRG).
J.P. was supported by the Cambridge doctoral training centre Mathematics of Information.
Acknowledgments
R.B. acknowledges the hospitality of the Department of Mathematics at McGill University where part of this work was carried out.
Citation
Roland Bauerschmidt. Jiwoon Park. Pierre-François Rodriguez. "The discrete Gaussian model, II. Infinite-volume scaling limit at high temperature." Ann. Probab. 52 (4) 1360 - 1398, July 2024. https://doi.org/10.1214/23-AOP1659
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