2024/12/06 by Joseph G. Conlon, Conlon, Joseph G., Michael Dabkowski +1
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Advanced Operator Algebra Research #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2412.05122
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.