Abstract:
I will explain what Gaussian multiplicative chaos (GMC) measures are, and prove new small deviations estimates for the total mass of GMC measures. Then I will show how to use GMC measures to construct the path integral formulation of the massless Sinh--Gordon model on the 2-dimensional torus. Finally, I will show how the small deviations bounds can be used to derive lower and upper bounds for the free energy of the massless Sinh--Gordon model on the infinite torus.
Based on joint work with Nikolay Barashkov (MPI Leipzig) and Mo Dick Wong (Durham).