Lecture notes on Gaussian multiplicative chaos and Liouville Quantum Gravity

Abstract

The purpose of these notes, based on a course given by the second author at Les Houches summer school, is to explain the probabilistic construction of Polyakov's Liouville quantum gravity using the theory of Gaussian multiplicative chaos. In particular, these notes contain a detailed description of the so-called Liouville measures of the theory and their conjectured relation to the scaling limit of large planar maps properly embedded in the sphere. These notes are rather short and require no prior knowledge on the topic.

References in corpus (3)

• Freezing and extreme value statistics in a Random Energy Model with logarithmically correlated potential
• Two perspectives of the 2D unit area quantum sphere and their equivalence
• Liouville Quantum Gravity on the Riemann sphere

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