MA2: Introduction to Logarithmically Correlated Fields and Multiplicative Chaos Measures

About

Logarithmically correlated random fields are stochastic processes that play an important role in various branches of modern probability theory such as probabilistic number theory, random matrix theory and euclidean quantum field theory. Many of their properties are best studied through associated random multi fractal measures known as multiplicative chaos measures. In this course, we will study the definitions and basic properties of logarithmically correlated random fields and multiplicative chaos measures as well as briefly discuss applications of the theory

Target group

Prerequisites for the course are a course on measure-theoretic probability and a basic course on functional analysis.

Advanced Bachelor’s students, Master’s students, PhD students and post-docs

Course aim

After the course, the student will
- Understand what kind of phenomena logarithmically correlated random fields are typically associated with.
- Be able to apply the theory of Gaussian multiplicative chaos to study fractal properties of logarithmically correlated Gaussian fields