Gaussian multiplicative chaos and KPZ duality

Understand

This paper is concerned with the construction of atomic Gaussian multiplicative chaos and the KPZ formula in Liouville quantum gravity.

• On the first hand, we construct purely atomic random measures corresponding to values of the parameter $\gamma^2$ beyond the transition phase (i.e.
• $\gamma^2>2d$) and check the duality relation with sub-critical Gaussian multiplicative chaos.
• On the other hand, we give a simplified proof of the classical KPZ formula as well as the dual KPZ formula for atomic Gaussian multiplicative chaos.