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arXiv · 2412.05122

Extensions of the Brascamp-Lieb Inequality and the Dipole Gas

Joseph G. Conlon·Michael Dabkowski
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Abstract

This paper is concerned with lattice field models in dimension at least 2. The action is a uniformly convex function of the gradient of the field. The main result Theorem 1.4 proves that charge-charge correlations in the Coulomb dipole gas are close to Gaussian. These results go beyond previous results of Dimock-Hurd and Conlon-Spencer. The approach in the paper is based on the observation that the sine-Gordon probability measure corresponding to the dipole gas is the invariant measure for a certain stochastic dynamics. The stochastic dynamics here differs from the stochastic dynamics in previous work used to study the problem.

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Joseph G. Conlon, Michael Dabkowski. 2024-12-06. Extensions of the Brascamp-Lieb Inequality and the Dipole Gas. https://arxiv.org/abs/2412.05122

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