发表机构
Università degli Studi di Padova; The Hong Kong University of Science and Technology（帕多瓦大学; 香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究超临界 Bernoulli 团簇上高斯自由场水平集与随机交织空置集的渗流相变，证明其在确定性临界水平发生非平凡相变，并发展了淬火树嵌入控制方法。
AI 中文摘要
我们考虑高斯自由场的水平集和随机交织的空置集，两者均定义在 $\mathbb{Z}^d$（$d \geq 3$）上超临界 Bernoulli 键渗流的无限团簇的典型实现上。我们证明，在 Bernoulli 键渗流的整个超临界区域中，高斯自由场的水平集和随机交织的空置集均在确定性的临界水平上经历非平凡的渗流相变。证明的一个关键方面是发展了关于树嵌入的某些淬火控制，从而允许在存在空间不规则性的情况下应用静态重整化方案，这可能具有独立的意义。
英文摘要
We consider the level sets of the Gaussian free field and the vacant set of random interlacements, both defined on a typical realization of the infinite cluster of supercritical Bernoulli bond percolation on $\mathbb{Z}^d$, $d \geq 3$. We prove that in the entire supercritical regime of Bernoulli bond percolation, both the level sets of the Gaussian free field and the vacant set of random interlacements undergo non-trivial percolation phase transitions at deterministic critical levels. A key aspect of the proof is the development of certain quenched controls over tree embeddings, permitting the application of a static renormalization scheme in the presence of spatial irregularities, which may be of independent interest.
Comments33 pages
