Minicourses

An introduction to Generic Chaining

Prof. Dr. Shahar Mendelson (The Australian National University)

Wednesday, 28 February, 10:15-12:00, HG G 43
Thursday, 07 March, 14:15-16:00, HG G 19.2
Friday, 22 March, 10:15-12:00, HG G 43

Wednesday, 10 April, 10:15 to 12:00, G 43
Wednesday, 10 April, 14:15 to 16:00, G 43
Monday, 29 April, 13:15 to 15:00, G 43
Thurday, 02 May 10:15 to 12:00, G 19.2

Abstract

Generic Chaining is a useful way of studying the behaviour of the supremum of a random process in terms of the structure of the set indexing the process. More accurately, if T is a set and \{X_t : t \in T\} is a collection of random variables, the goal is to find upper and lower bounds on \sup_{t \in T} X_t in terms of the "geometry" of T (though the meaning of "geometry" here isn't obvious, seeing that T has no apparent structure).

In this mini course I will present Talagrand's characterisation of the expected supremum of a gaussian process; explain the difficulties that arise when trying to establish a similar result for Bernoulli processes; and if time permits, show more sophisticated chaining techniques that are needed in some applications (e.g. for the study of the extremal singular values of random matrices and for embedding results).