MATJ5121 MA2: Introduction to Logarithmically Correlated Fields and Multiplicative Chaos Measures (JSS34) (2 cr)
Study level:
Postgraduate studies
Grading scale:
Pass - fail
Language:
English
Responsible organisation:
Faculty of Mathematics and Science
Curriculum periods:
2025-2026
Description
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.
Learning outcomes
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.
Description of prerequisites
Prerequisites for the course are a course on measure-theoretic probability and a basic course on functional analysis.
Completion methods
Method 1
Description:
The course consists of 10 hours of lectures and it can be passed by solving exercise problems, writing an essay, or through a simulation project.
Evaluation criteria:
Pass/fail
Time of teaching:
Period 1
Select all marked parts
Parts of the completion methods
x
Participation in teaching (2 cr)
Type:
Participation in teaching
Grading scale:
Pass - fail
Evaluation criteria:
<p>Pass/fail</p>
Language:
English
Study methods:
The course consists of 10 hours of lectures and it can be passed by solving exercise problems, writing an essay, or through a simulation project.