We study the distribution of the maximum of a large class of Gaussian fields indexed by a box and possessing logarithmic correlations up to local defects that are sufficiently rare. Under appropriate assumptions that generalize those in Ding et al., we show that asymptotically, the centered maximum of the field has a randomly-shifted Gumbel distribution. We prove that the two dimensional Gaussian free field on a super-critical bond percolation cluster with close enough to 1, as well as the Gaussian free field in i.i.d. bounded conductances, fall under the assumptions of our general theorem.

中文翻译：

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随机环境中对数相关高斯场的最大值

我们研究由框索引的一大类高斯场的最大值的分布并具有与足够罕见的局部缺陷的对数相关性。在概括 Ding 等人的假设的适当假设下，我们表明渐进地，场的中心最大值具有随机移位的 Gumbel 分布。我们证明了超临界键渗流簇上的二维高斯自由场足够接近 1，以及独立同分布电导的高斯自由场，都属于我们一般定理的假设。