Random Fourier series, Gaussian free fields and related topics, spring 2009

Note:

Last lecture for the original course is 20.3 Friday, since next week there is the overlapping
 workshop on related topics (and on Friday morning Dario will tell us about Brownian excursions).
 Lectures will continue on the GFF in May and perhaps later on (August/fall) as a free seminar
 type thing. We just have to agree on each time on the schedule separately.

Lecturer

Eero Saksman

Scope

10 cu.

Type and prerequisites

Advanced studies.
 Knowledge on basic probability theory is assumed, including conditional expectations. Familiarity with rudimentary facts on Brownian motion is preferable, but not absolutely necessary. Basic functional analysis and harmonic analysis is expected. Familiarity with generalized functions would be helpful, but again is not crucial.

Lectures

Basically weeks 4, 6--13, note that FIRST LECTURE is on Tuesday 20.1. Other small deviations will be announced during the lectures.

Tue 14-16 C124
 Wed 12-14 C123
 Fri 10-12 C123

Contents

We will study basic properties of random Fourier series and random fields, mainly concentrating on the Gaussian case. Special emphasis will be on Gaussian free fields (GFF), and the corresponding exponential process that plays an interesting role in recent research of e.g. quantum gravity. If time permits we will also consider other topics such as random quasiconformal maps.

Registration

Registration at the first lecture.

Exercises and exam

There are no exercise classes, the course can be passed through an exam or by writing a small essay on a suitable topic.