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Gaussian multiplicative chaos through the lens of the 2D Gaussian free field

2017/09/13 by Aru, Juhan
#60G15 #60G57 #60G60 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1709.04355

Abstract

The aim of this review-style paper is to provide a concise, self-contained and unified presentation of the construction and main properties of Gaussian multiplicative chaos (GMC) measures for log-correlated fields in 2D in the subcritical regime. By considering the case of the 2D Gaussian free field, we review convergence, uniqueness and characterisations of the measures; revisit Kahane's convexity inequalities and existence and scaling of moments; discuss the measurability of the underlying field with respect to the GMC measure and present a KPZ relation for scaling exponents.

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