The intermediate level-sets of the four-dimensional membrane model
Probability
2025-09-22 v2
Abstract
In this paper, we consider the discrete membrane model in four dimensions. We confirm the existence of the scaling limit of the intermediate (i.e., a multiple of the expected maximum) level-sets of the model, and show that it is equal in law to the sub-critical Gaussian multiplicative chaos (GMC) measure of the continuum membrane model.
Keywords
Cite
@article{arxiv.2205.03621,
title = {The intermediate level-sets of the four-dimensional membrane model},
author = {Xinyi Li and Runsheng Liu},
journal= {arXiv preprint arXiv:2205.03621},
year = {2025}
}
Comments
22 pages, accepted by Acta Mathematica Sinica, English Series