The intermediate level-sets of the four-dimensional membrane model

2022/05/07 by Li, Xinyi, Liu, Runsheng · 1 citation
#60G15 #60G60 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2205.03621

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.

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• Full extremal process in four-dimensional membrane model

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