Gaussian Multiplicative Chaos Through the Lens of the 2D Gaussian Free Field
2020, v.26, Issue 1, 17-56
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.
Keywords: Gaussian multiplicative chaos, Gaussian free field, Liouville measure, KPZ relation