标题： Brascamp-Lieb不等式的扩展和偶极子气体 显示英文标题

标题： Extensions of the Brascamp-Lieb Inequality and the Dipole Gas

摘要： 本文研究至少二维的格点场模型。 作用量是场梯度的均匀凸函数。 主要结果定理1.4证明了库仑偶极子气体中的电荷-电荷相关性接近高斯分布。 这些结果超越了Dimock-Hurd和Conlon-Spencer之前的成果。 本文的方法基于一个观察，即对应于偶极子气体的正弦-戈登概率测度是某种随机动力学的不变测度。 这里的随机动力学与之前用于研究该问题的随机动力学不同。 显示英文摘要

摘要： 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.