The majorizing measure theorem of Talagrand provides a sharp description

of the expected supremum of any Gaussian process in terms of the geometry

of its index set. It plays a fundamental role in various problems in

probability theory and functional analysis. However, this deep result has

the reputation of being notoriously delicate and difficult to use. In this

talk, I will show a new proof of the majorizing measure theorem that is

completely elementary. More importantly, the two basic ingredients on

which this proof is based--a simple contraction principle and an

interpolation method--provide a powerful mechanism for bounding the

suprema of Gaussian processes in concrete situations. If time permits, I

will sketch an application to the norms of inhomogeneous random matrices.

# An elementary proof of the majorizing measure theorem

Date:

Tuesday, January 31, 2017 - 2:00pm

Location:

Math Sci 111

Speaker:

Ramon van Handel

(Princeton)

Event Type: