Summary: Seminar in Probability and Stochastic Processes 098435
First Meeting: Wednesday 9.3.2005 12:30-14:30 Room 152 IE
Three topics we intend to cover are:
Stochastic Geometry of Interacting Spin Systems
Lecture 1: Curie-Weiss mean field model: Formulation, phase transition, limit the-
Lecture 2:. Sparse random graphs: Emergence of the giant component.
Lecture 3:. Random graph representation of the Curie-Weiss model. Continuous
time random graphs and quantum versions of the Curie-Weiss model.
Some problems in Gaussian processes and some problems in
Lecture 1: About maxima and geometry. Expansions of Gaussian processes, Poincare's
limit theorem a la Diaconis, Gaussian processes and the infinite dimensional unit
Lecture 2: Lipshitz-Killing curvatures. Tube formulae and the fundamental kine-
matic formula on spheres. Minkowski functionals on Gauss space.
Lecture 3: A Gaussian kinematic formula. Back to maxima and geometry.