论文标题
随机环境中的对数相关的高斯字段的最大值
The maximum of log-correlated Gaussian fields in random environments
论文作者
论文摘要
我们研究了由盒子$ v_n \ subset z^d $索引的大型高斯田地的最大分布，并具有对数相关性，直到局部缺陷，而对数足够罕见的局部缺陷。在适当的假设下，Roy和Zeitouni概括的人（Annals Probab。（45）2017，3886-3928），我们表明，渐近地表明，该田间的最大最大值具有随机变形的gumbel分布。我们证明，在超临界债券渗透集群中，$ p $的二维高斯免费场和I.I.D的高斯免费场均足够接近$ 1 $。有限的电导，属于我们一般定理的假设。
We study the distribution of the maximum of a large class of Gaussian fields indexed by a box $V_N\subset Z^d$ and possessing logarithmic correlations up to local defects that are sufficiently rare. Under appropriate assumptions that generalize those in Ding, Roy and Zeitouni (Annals Probab. (45) 2017, 3886-3928), 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 $p$ 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.
