论文标题
2D离散高斯模型在高温下的多点函数的中央限制定理
Central Limit Theorem for Multi-Point Functions of the 2D Discrete Gaussian Model at high temperature
论文作者
论文摘要
我们使用rnormalisation Grout方法研究了离散高斯模型（即，高斯自由场限制在高温度下）的显微镜观察值。 In particular, we show the central limit theorem for the two-point function of the Discrete Gaussian model by computing the asymptotic of the moment generating function $\langle e^{z (σ(0) - σ(y))} \rangle_{β, \mathbb{Z}^2}^{\dg}$ for $z \in \mathbb{C}$足够小。我们使用的方法与\ cite {dgauss1，dgauss2}中使用的多尺度聚合物膨胀的直接连接，该方法用于研究离散高斯模型的缩放限制。该方法还适用于在\ cite {MR634447}中研究的正弦戈登类型的多点函数和晶格模型。
We study microscopic observables of the Discrete Gaussian model (i.e., the Gaussian free field restricted to take integer values) at high temperature using the renormalisation group method. In particular, we show the central limit theorem for the two-point function of the Discrete Gaussian model by computing the asymptotic of the moment generating function $\langle e^{z (σ(0) - σ(y))} \rangle_{β, \mathbb{Z}^2}^{\dg}$ for $z \in \mathbb{C}$ sufficiently small. The method we use has direct connection with the multi-scale polymer expansion used in \cite{dgauss1, dgauss2}, where it was used to study the scaling limit of the Discrete Gaussian model. The method also applies to multi-point functions and lattice models of sine-Gordon type studied in \cite{MR634447}.
