论文标题
二维规模抗偶联的离散高斯自由领域的极端：弱相关的极端过程
Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: Extremal process in the weakly correlated regime
论文作者
论文摘要
我们证明，在弱相关性方面，二维规模侵权性高斯自由场的全部极端过程的融合。从2D离散高斯自由场通过函数$ \ MATHCAL {i}修改差异，从2D离散高斯免费字段获得了比例征用均匀的离散高斯免费字段：[0,1] \ rightArrow [0,1] $。限制过程是集群COX过程。 COX过程的随机强度取决于通过随机度量$ y $以及$ \ Mathcal {i}^\ prime（1）$通过常数$β$通过随机度量$ y $和$ \ mathcal {i}^\ prime（0）$。我们将群集过程描述，该过程仅取决于$ \ Mathcal {i}^\ prime（1）$，是标准2D离散高斯免费场的点，条件异常高。
We prove convergence of the full extremal process of the two-dimensional scale-inhomogeneous discrete Gaussian free field in the weak correlation regime. The scale-inhomogeneous discrete Gaussian free field is obtained from the 2d discrete Gaussian free field by modifying the variance through a function $\mathcal{I}:[0,1]\rightarrow [0,1]$. The limiting process is a cluster Cox process. The random intensity of the Cox process depends on the $\mathcal{I}^\prime(0)$ through a random measure $Y$ and on the $\mathcal{I}^\prime(1)$ through a constant $β$. We describe the cluster process, which only depends on $\mathcal{I}^\prime(1)$, as points of a standard 2d discrete Gaussian free field conditioned to be unusually high.
