




























We investigate the extremal process of four-dimensional membrane models as the size of the lattice $N$ tends to infinity. We prove the cluster-like geometry of the extreme points and the existence as well as the uniqueness of the extremal process. The extremal process is characterized by a distributional invariance property and a Poisson structure with explicit formulas. Our approach follows the same philosophy as the two-dimensional Gaussian free field (2D GFF) via the comparison with the modified branching random walk. The proofs leverage the ``Dysonization'' technique and a careful treatment of the correlation structure, which is more intricate than the 2D GFF case. As a by-product, we also obtain a simpler proof of a crucial sprinkling lemma.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。