MATJ5121 MA2: Introduction to Logarithmically Correlated Fields and Multiplicative Chaos Measures (JSS34) (2 op)
Opinnon taso:
Jatko-opinnot
Arviointiasteikko:
Hyväksytty - hylätty
Suorituskieli:
englanti
Vastuuorganisaatio:
Matemaattis-luonnontieteellinen tiedekunta
Opetussuunnitelmakaudet:
2025-2026
Kuvaus
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.
Osaamistavoitteet
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.
Esitietojen kuvaus
Prerequisites for the course are a course on measure-theoretic probability and a basic course on functional analysis.
Suoritustavat
Tapa 1
Kuvaus:
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.
Arviointiperusteet:
Pass/fail
Opetusajankohta:
Periodi 1
Valitaan kaikki merkityt osat
Suoritustapojen osat
x
Osallistuminen opetukseen (2 op)
Tyyppi:
Osallistuminen opetukseen
Arviointiasteikko:
Hyväksytty - hylätty
Arviointiperusteet:
<p>Pass/fail</p>
Suorituskieli:
englanti
Työskentelytavat:
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.