Student Probability Seminar

In this talk we give a gentle introduction to Gaussian multiplicative chaos which has received a lot of attention recently through its link to thick points of Gaussian fields and 'Liouville Quantum Gravity’. Informally speaking Gaussian multiplicative chaos is trying to make sense of a measure that is proportional to exp(\gamma X(x))dx, where X(x) is a log correlated Gaussian field.

We follow an article ‘An elementary approach to Gaussian multiplicative chaos' by N. Berestycki which gives a short and self-contained approach to Gaussian multiplicative chaos. We will try to answer the following two main questions: How can we give a ‘good’ definition of Gaussian multiplicative chaos using approximations? Under which conditions is the limiting object nontrivial?