An elementary proof of the majorizing measure theorem

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.