In this thesis, we study the extreme values of certain log-correlated random fields that are
Gaussian (the scale-inhomogeneous Gaussian free field and the time-inhomogeneous …

This work aims to extend the existing results on thick points of logarithmic-correlated
Gaussian Free Fields to Gaussian random fields that are more singular. To be specific, we …

This work aims to extend the existing results on the Hausdorff dimension of the classical
thick point sets to a more general class of exceptional sets of a Gaussian free field (GFF). We …

In this work, we regularize Gaussian free fields based on the Fourier-Bessel expansion to
extend part of the results on the Liouville quantum gravity measure and the KPZ relation in …

The geometry of the continuum Gaussian free field (GFF) has been studied extensively. In
particular, Hu, Miller, and Peres proved that the Hausdorff dimension of the a-thick point set …

This thesis consists of two distinct parts. In the first part, we treat two different models of
Gaussian Fields: one is the membrane model at its critical dimension, of which we establish …