Localization of Random Surfaces with Monotone Potentials and an
FKG-Gaussian Correlation Inequality
Localization of Random Surfaces with Monotone Potentials and an
FKG-Gaussian Correlation Inequality
The seminal 1975 work of Brascamp-Lieb-Lebowitz initiated the rigorous study of Ginzberg-Landau random surface models. It was conjectured therein that fluctuations are localized on $\mathbb Z^d$ when $d\geq 3$ for very general potentials, matching the behavior of the Gaussian free field. We confirm this behavior for all even potentials $U:\mathbb …