Introduction to Gaussian fields and multiplicative chaos, spring 2017
Introduction to Gaussian fields and multiplicative chaos, spring 2017
Teacher: Eero Saksman
Scope: 10 cr
Type: Advanced studies
Teaching: Lectures (Mo 1012), Tu 1214 and We 1012 C124 at Exactum. First lecture on Tuesday 17.1.17.
Topics: Gaussian fields are fundamental objects that play an important role in many different connections. They are used extensively e.g. inside various branches of mathematics, in stochastic modelling, and many areas of mathematical physics including scaling limits of lattice models like SLE.
The aim of the first part of the course is to provide the basic ingredients of the general theory of Gaussian random fields. The second part aims somewhat deeper and e.g. discusses in more detail basic properties of Gaussian free fields. Finally, the course ends by giving an introduction to multiplicative chaos. These fascinating measures appear in e.g. in connection with scaling limits of statistical physics, mathematical finance, turbulence, and quantum gravity. If time permits, we will describe how they appear also in connection with the Riemann zeta function.
Prerequisites: Probability theory 1 and 2 (not all of the material is needed), or equivalent knowledge.
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Exercises
Teaching schedule
Most of the weeks 39 and 1118, (Mondays 1012), Tuesdays 1214 and Wednesdays 1012 in room C124.
Easter holiday 13.19.4.
Passing the course
The course can be passed by attending (most of) the lectures and returning in a written form a portion (around 50 %) of the given exercises. Alternatively, the exercises can be replaced by a written essay on a topic agreed on with the lecturer.
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