Description of the course:

Gaussian processes will be the basic object in this course. Starting with classical comparison theorems, our work will culminate in majorizing measures (nothing to do with measure theory!), a glass through which we look now at all bounded Gaussian processes. Applications will bring us to the convex geometry, clarifying also an extremely difficult result of Bourgain in Harmonic Analysis (Lambda-p problem).

I expect that some of our meetings will be in a seminar form, where somebody will present a topic, along with all the difficulties which we will try to resolve, etc.

Prerequisites:

standard probability and functional analysis.

There will be 12 lectures, one per week (on Thursdays 16:15 - 18:15 room 261),
starting March 15 and finishing June 7 (excluding the Independence day, April 26).

I will keep posting readable notes for each lecture. Each set of notes
contains the (most important) notions and results, and also all exercises for
the current lecture. Solving the exercises is not required but highly desirable
to develop intuition.
 

Independent Random Variables
Lecture 1  (March 15)
Lecture 2  (March 22)
Lecture 3  (March 29)
Lecture 4  (April 5)
No lecture (April 12) - Pesach
Lecture 5  (April 19)

Random Processes
Lecture 6  (May 3)
Lecture 7  (May 10)
Lecture 8  (May 17)
Lecture 9  (May 24)
Lecture 10  (May 24)
 

FINAL HOMEWORK: Due July 11, 2001
 

Literature:

M. Talagrand, Majorizing measures: the generic chaining. Ann. Probab. 24 (1996), no. 3, 1049--1103
J.-P. Kahane, Some random series of functions. Library codes 519.2 KAH, 519.28 KAH
M. Ledoux, M. Talagrand. Probability in Banach spaces. Library code 519.2-LED