Mo Dick Wong

Power Variations of Critical Gaussian Multiplicative Chaos and Spectral Applications

In this talk, I will discuss a natural connection between critical and supercritical Gaussian multiplicative chaos (GMC) through power variations. This relation allows us to identify the optimal exponent in a logarithmic-type modulus of continuity for critical GMC. As a consequence, we show that the formal Laplace–Beltrami operator associated with a critical Liouville quantum gravity surface has non-empty essential spectrum almost surely. If time permits, I will also describe an application to the Fourier decay of critical GMC.