The aim of this course is to carry on the study of Brownian motion after the Graduate course "Brownian motion" in Semester 1, 2011/2012. The material we cover includes Hausdorff dimension, potential theory of Brownian motion, intersections and self-intersections of Brownian paths and exceptional sets for Brownian motion.
We follow Peter Mörters and Yuval Peres' book "Brownian motion", which is a readable and formally self-contained account of the theory. The book can be downloaded from Peter Mörters' website
The group is organised by Maren Eckhoff. Everybody is welcome to attend.
The course takes place on Wednesdays 09.15-11.05 in the Wolfson lecture theatre 4W 1.7 unless stated otherwise. If you would like to present one of the lectures, please contact the organiser.
8.February: Hausdorff dimension & the energy method (Ch.4.1/4.3) - Maren Eckhoff
15.February: Frostman's lemma & Riesz capacity (Ch.4.4) - Chris Daniels
22.February: The Dirichlet problem & Recurrence/Transience of Brownian motion (Ch.3.1/3.2/8.1) - Alex Watson
29.February: Occupation measures & Green functions (Ch.3.3) - Curdin Ott
7.March: Polar sets, capacities & Kakutani's theorem (Ch.8.3) - Maren Eckhoff
14.March: Intersections of Brownian paths (Ch.9.1) - Christoph Höggerl
21.March: Intersection equivalence and percolation limit sets (Ch.9.2) - Marion Hesse
28.March: No lecture - Easter Probability Meeting at the University of Warwick
18.April: Multiple points of Brownian paths (Ch.9.3) - Horacio Gonzalez
25.April: Fast times of Brownian motion (Ch.5.1/10.1) - Albert Ferreiro-Castilla
2.May: Limsup fractals (Ch.10.1/10.2) - Christian Mönch
9.May, Changed time: 14.15-16.05 : The harmonic measure (Ch.3.4) - Piotr Milos
Prerequisites: Basic knowledge about Brownian motion is required, roughly on the level of Chapter 1 and 2 of the course book. Please get in touch if you are unsure.